The study of functions, mechanisms of generation, and pathways of movement of cerebral fluids has... more The study of functions, mechanisms of generation, and pathways of movement of cerebral fluids has a long history, but the last decade has been especially productive. The proposed glymphatic hypothesis, which suggests a mechanism of the brain waste removal system (BWRS), caused an active discussion on both the criticism of some of the perspectives and our intensive study of new experimental facts. It was especially found that the intensity of the metabolite clearance changes significantly during the transition between sleep and wakefulness. Interestingly, at the cellular level, a number of aspects of this problem have been focused on, such as astrocytes–glial cells, which, over the past two decades, have been recognized as equal partners of neurons and perform many important functions. In particular, an important role was assigned to astrocytes within the framework of the glymphatic hypothesis. In this review, we return to the “astrocytocentric” view of the BWRS function and the expl...
The global number of people with Alzheimer’s disease (AD) doubles every 5 years. It has been esta... more The global number of people with Alzheimer’s disease (AD) doubles every 5 years. It has been established that unless an effective treatment for AD is found, the incidence of AD will triple by 2060. However, pharmacological therapies for AD have failed to show effectiveness and safety. Therefore, the search for alternative methods for treating AD is an urgent problem in medicine. The lymphatic drainage and removal system of the brain (LDRSB) plays an important role in resistance to the progression of AD. The development of methods for augmentation of the LDRSB functions may contribute to progress in AD therapy. Photobiomodulation (PBM) is considered to be a non-pharmacological and safe approach for AD therapy. Here, we highlight the most recent and relevant studies of PBM for AD. We focus on emerging evidence that indicates the potential benefits of PBM during sleep for modulation of natural activation of the LDRSB at nighttime, providing effective removal of metabolites, including a...
The deposition of amyloid-β (Aβ) in the brain is a risk factor for Alzheimer’s disease (AD). Ther... more The deposition of amyloid-β (Aβ) in the brain is a risk factor for Alzheimer’s disease (AD). Therefore, new strategies for the stimulation of Aβ clearance from the brain can be useful in preventing AD. Transcranial photostimulation (PS) is considered a promising method for AD therapy. In our previous studies, we clearly demonstrated the PS-mediated stimulation of lymphatic clearing functions, including Aβ removal from the brain. There is increasing evidence that sleep plays an important role in Aβ clearance. Here, we tested our hypothesis that PS at night can stimulate Aβ clearance from the brain more effectively than PS during the day. Our results on healthy mice show that Aβ clearance from the brain occurs faster at night than during wakefulness. The PS course at night improves memory and reduces Aβ accumulation in the brain of AD mice more effectively than the PS course during the day. Our results suggest that night PS is a more promising candidate as an effective method in preve...
This paper presents a novel approach for analyzing the structural properties of time series from ... more This paper presents a novel approach for analyzing the structural properties of time series from realworld complex systems by means of evolving complex networks. Starting from the concept of recurrences in phase space, the recurrence matrices corresponding to different parts of a time series are re-interpreted as the adjacency matrices of complex networks, which link different observations if the associated temporal evolution is sufficiently similar. We provide some illustrative examples demonstrating that the local properties of the resulting recurrence networks allow identifying dynamically invariant objects in the phase space of complex systems. Moreover, changes in the global network properties of evolving recurrence networks allow identifying time intervals containing hidden dynamical transitions, which is exemplified for some financial time series.
The asymptotic behaviour of dynamical processes in networks can be expressed as a function of spe... more The asymptotic behaviour of dynamical processes in networks can be expressed as a function of spectral properties of the Adjacency and Laplacian matrices. Although many theoretical results are known for the spectra of traditional configuration models, networks generated through these models fail to describe many topological features of real-world networks, in particular non-null values for the clustering coefficient. Here we study the effects of cycles or order three (triangles) in network spectra. By using recent advances in random matrix theory, we determine the spectrum distribution of the network Adjacency matrix as a function of the average number of triangles attached to each node for networks without modular structure and degree-degree correlations. Furthermore we show that cycles of order three have a weak influence on the Laplacian eigenvalues, fact that explains the recent controversy on the dynamics of clustered networks. Our findings can shed light in the study of how pa...
2020 and 2021 have been unprecedented years due to the rapid spread of the modified severe acute ... more 2020 and 2021 have been unprecedented years due to the rapid spread of the modified severe acute respiratory syndrome coronavirus around the world. The coronavirus disease 2019 (COVID-19) causes atypical infiltrated pneumonia with many neurological symptoms, and major sleep changes. The exposure of people to stress, such as social confinement and changes in daily routines, is accompanied by various sleep disturbances, known as ‘coronasomnia’ phenomenon. Sleep disorders induce neuroinflammation, which promotes the blood–brain barrier (BBB) disruption and entry of antigens and inflammatory factors into the brain. Here, we review findings and trends in sleep research in 2020–2021, demonstrating how COVID-19 and sleep disorders can induce BBB leakage via neuroinflammation, which might contribute to the ‘coronasomnia’ phenomenon. The new studies suggest that the control of sleep hygiene and quality should be incorporated into the rehabilitation of COVID-19 patients. We also discuss persp...
IEEE Journal of Selected Topics in Quantum Electronics, 2021
In this review, we discuss the crucial role of cranial and the extracranial lymphatics in keeping... more In this review, we discuss the crucial role of cranial and the extracranial lymphatics in keeping the central nervous system (CNS) health. We talk about the important lymphatic mechanism of removal of metabolites and toxins from the brain, which orchestrates the regenerative processes in CNS. We debate a novel knowledge about the lymphatic mechanism responsible for maintaining the balance between the exit and the entrance of Manuscript
Cerebral small vessel disease (CSVD) is a leading cause of cognitive decline in elderly people an... more Cerebral small vessel disease (CSVD) is a leading cause of cognitive decline in elderly people and development of Alzheimer’s disease (AD). Blood–brain barrier (BBB) leakage is a key pathophysiological mechanism of amyloidal CSVD. Sleep plays a crucial role in keeping health of the central nervous system and in resistance to CSVD. The deficit of sleep contributes to accumulation of metabolites and toxins such as beta-amyloid in the brain and can lead to BBB disruption. Currently, sleep is considered as an important informative platform for diagnosis and therapy of AD. However, there are no effective methods for extracting of diagnostic information from sleep characteristics. In this review, we show strong evidence that slow wave activity (SWA) (0–0.5 Hz) during deep sleep reflects glymphatic pathology, the BBB leakage and memory deficit in AD. We also discuss that diagnostic and therapeutic targeting of SWA in AD might lead to be a novel era in effective therapy of AD. Moreover, we ...
IEEE transactions on neural networks and learning systems, 2012
In this paper, a new control strategy is proposed for the synchronization of stochastic dynamical... more In this paper, a new control strategy is proposed for the synchronization of stochastic dynamical networks with nonlinear coupling. Pinning state feedback controllers have been proved to be effective for synchronization control of state-coupled dynamical networks. We will show that pinning impulsive controllers are also effective for synchronization control of the above mentioned dynamical networks. Some generic mean square stability criteria are derived in terms of algebraic conditions, which guarantee that the whole state-coupled dynamical network can be forced to some desired trajectory by placing impulsive controllers on a small fraction of nodes. An effective method is given to select the nodes which should be controlled at each impulsive constants. The proportion of the controlled nodes guaranteeing the stability is explicitly obtained, and the synchronization region is also derived and clearly plotted. Numerical simulations are exploited to demonstrate the effectiveness of th...
Physical review. E, Statistical, nonlinear, and soft matter physics, 2009
Stability of synchronization in unidirectionally coupled time-delay systems is studied using the ... more Stability of synchronization in unidirectionally coupled time-delay systems is studied using the Krasovskii-Lyapunov theory. We have shown that the same general stability condition is valid for different cases, even for the general situation (but with a constraint) where all the coefficients of the error equation corresponding to the synchronization manifold are time dependent. These analytical results are also confirmed by the numerical simulation of paradigmatic examples.
The effect of stirring in an inhomogeneous oscillatory medium is investigated. We show that the s... more The effect of stirring in an inhomogeneous oscillatory medium is investigated. We show that the stirring rate can control the macroscopic behavior of the system producing collective oscillations (synchronization) or complete quenching of the oscillations (oscillator death). We interpret the homogenization rate due to mixing as a measure of global coupling and compare the phase diagrams of stirred oscillatory media and of populations of globally coupled oscillators.
Though the notion of phase synchronization has been well studied in chaotic dynamical systems wit... more Though the notion of phase synchronization has been well studied in chaotic dynamical systems without delay, it has not been realized yet in chaotic time-delay systems exhibiting non-phase coherent hyperchaotic attractors. In this article we report the first identification of phase synchronization in coupled time-delay systems exhibiting hyperchaotic attractor. We show that there is a transition from non-synchronized behavior to phase and then to generalized synchronization as a function of coupling strength. These transitions are characterized by recurrence quantification analysis, by phase differences based on a new transformation of the attractors and also by the changes in the Lyapunov exponents. We have found these transitions in coupled piece-wise linear and in Mackey-Glass time-delay systems.
We report the identification of global phase synchronization (GPS) in a linear array of unidirect... more We report the identification of global phase synchronization (GPS) in a linear array of unidirectionally coupled Mackey-Glass time-delay systems exhibiting highly non-phase-coherent chaotic attractors with complex topological structure. In particular, we show that the dynamical organization of all the coupled time-delay systems in the array to form GPS is achieved by sequential synchronization as a function of the coupling strength. Further, the asynchronous ones in the array with respect to the main sequentially synchronized cluster organize themselves to form clusters before they achieve synchronization with the main cluster. We have confirmed these results by estimating instantaneous phases including phase difference, average phase, average frequency, frequency ratio and their differences from suitably transformed phase coherent attractors after using a nonlinear transformation of the original non-phase-coherent attractors. The results are further corroborated using two other independent approaches based on recurrence analysis and the concept of localized sets from the original non-phase-coherent attractors directly without explicitly introducing the measure of phase.
We study synchronous behavior in ensembles of locally coupled nonidentical Bonhoeffer-van der Pol... more We study synchronous behavior in ensembles of locally coupled nonidentical Bonhoeffer-van der Pol oscillators. We show that, in a chain of N elements not less than 2 N−1 , different coexisting regimes of global synchronization are possible, and we investigate wave-induced synchronous regimes in a chain and in a lattice of coupled nonidentical Bonhoeffer-van der Pol oscillators.
We present an automatic control method for phase locking of regular and chaotic non-identical osc... more We present an automatic control method for phase locking of regular and chaotic non-identical oscillations, when all subsystems interact via feedback. This method is based on the well known principle of feedback control which takes place in nature and is successfully used in engineering. In contrast to unidirectional and bidirectional coupling, our approach supposes the existence of a special controller, whose input is given by a quadratic form of the coordinates of the individual systems and its output is a result of the application of a linear differential operator. Using several examples we demonstrate the effectiveness of our approach to achieve controlled phase synchronization.
This review provides a summary of methods originated in (non-equilibrium) statistical mechanics a... more This review provides a summary of methods originated in (non-equilibrium) statistical mechanics and information theory, which have recently found successful applications to quantitatively studying complexity in various components of the complex Entropy 2013, 15 4845 system Earth. Specifically, we discuss two classes of methods: (i) entropies of different kinds (e.g., on the one hand classical Shannon and Rényi entropies, as well as non-extensive Tsallis entropy based on symbolic dynamics techniques and, on the other hand, approximate entropy, sample entropy and fuzzy entropy); and (ii) measures of statistical interdependence and causality (e.g., mutual information and generalizations thereof, transfer entropy, momentary information transfer). We review a number of applications and case studies utilizing the above-mentioned methodological approaches for studying contemporary problems in some exemplary fields of the Earth sciences, highlighting the potentials of different techniques.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2008
The notion of phase synchronization in time-delay systems, exhibiting highly non-phase-coherent a... more The notion of phase synchronization in time-delay systems, exhibiting highly non-phase-coherent attractors, has not been realized yet even though it has been well studied in chaotic dynamical systems without delay. We report the identification of phase synchronization in coupled nonidentical piecewise linear and in coupled Mackey–Glass time-delay systems with highly non-phase-coherent regimes. We show that there is a transition from nonsynchronized behavior to phase and then to generalized synchronization as a function of coupling strength. We have introduced a transformation to capture the phase of the non-phase-coherent attractors, which works equally well for both the time-delay systems. The instantaneous phases of the above coupled systems calculated from the transformed attractors satisfy both the phase and mean frequency locking conditions. These transitions are also characterized in terms of recurrence-based indices, namely generalized autocorrelation function P(t), correlati...
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2009
Transitions between inverse anticipatory, inverse complete, and inverse lag synchronizations are ... more Transitions between inverse anticipatory, inverse complete, and inverse lag synchronizations are shown to occur as a function of the coupling delay in unidirectionally coupled time-delay systems with inhibitory coupling. We have also shown that the same general asymptotic stability condition obtained using the Krasovskii–Lyapunov functional theory can be valid for the cases where (i) both the coefficients of the Δ(t) (error variable) and Δτ=Δ(t−τ) (error variable with delay) terms in the error equation corresponding to the synchronization manifold are time independent and (ii) the coefficient of the Δ term is time independent, while that of the Δτ term is time dependent. The existence of different kinds of synchronization is corroborated using similarity function, probability of synchronization, and also from changes in the spectrum of Lyapunov exponents of the coupled time-delay systems.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2004
In the last decade, there has been an increasing interest in compensating thermally induced error... more In the last decade, there has been an increasing interest in compensating thermally induced errors to improve the manufacturing accuracy of modular tool systems. These modular tool systems are interfaces between spindle and workpiece and consist of several complicatedly formed parts. Their thermal behavior is dominated by nonlinearities, delay and hysteresis effects even in tools with simpler geometry and it is difficult to describe it theoretically. Due to the dominant nonlinear nature of this behavior the so far used linear regression between the temperatures and the displacements is insufficient. Therefore, in this study we test the hypothesis whether we can reliably predict such thermal displacements via nonlinear temperature-displacement regression functions. These functions are estimated first from learning measurements using the alternating conditional expectation (ACE) algorithm and then tested on independent data sets. First, we analyze data that were generated by a finite ...
We present recently introduced new recurrence plot based measures of complexity and illustrate th... more We present recently introduced new recurrence plot based measures of complexity and illustrate their potential with applications to the logistic map and heart rate variability data. These new measures make the identification of chaos-chaos transitions possible and identify laminar states. The application to the heart rate variability data detects and quantifies the laminar phases before a lifethreatening cardiac arrhythmia occurs; thereby facilitating a prediction of such an event.
The study of functions, mechanisms of generation, and pathways of movement of cerebral fluids has... more The study of functions, mechanisms of generation, and pathways of movement of cerebral fluids has a long history, but the last decade has been especially productive. The proposed glymphatic hypothesis, which suggests a mechanism of the brain waste removal system (BWRS), caused an active discussion on both the criticism of some of the perspectives and our intensive study of new experimental facts. It was especially found that the intensity of the metabolite clearance changes significantly during the transition between sleep and wakefulness. Interestingly, at the cellular level, a number of aspects of this problem have been focused on, such as astrocytes–glial cells, which, over the past two decades, have been recognized as equal partners of neurons and perform many important functions. In particular, an important role was assigned to astrocytes within the framework of the glymphatic hypothesis. In this review, we return to the “astrocytocentric” view of the BWRS function and the expl...
The global number of people with Alzheimer’s disease (AD) doubles every 5 years. It has been esta... more The global number of people with Alzheimer’s disease (AD) doubles every 5 years. It has been established that unless an effective treatment for AD is found, the incidence of AD will triple by 2060. However, pharmacological therapies for AD have failed to show effectiveness and safety. Therefore, the search for alternative methods for treating AD is an urgent problem in medicine. The lymphatic drainage and removal system of the brain (LDRSB) plays an important role in resistance to the progression of AD. The development of methods for augmentation of the LDRSB functions may contribute to progress in AD therapy. Photobiomodulation (PBM) is considered to be a non-pharmacological and safe approach for AD therapy. Here, we highlight the most recent and relevant studies of PBM for AD. We focus on emerging evidence that indicates the potential benefits of PBM during sleep for modulation of natural activation of the LDRSB at nighttime, providing effective removal of metabolites, including a...
The deposition of amyloid-β (Aβ) in the brain is a risk factor for Alzheimer’s disease (AD). Ther... more The deposition of amyloid-β (Aβ) in the brain is a risk factor for Alzheimer’s disease (AD). Therefore, new strategies for the stimulation of Aβ clearance from the brain can be useful in preventing AD. Transcranial photostimulation (PS) is considered a promising method for AD therapy. In our previous studies, we clearly demonstrated the PS-mediated stimulation of lymphatic clearing functions, including Aβ removal from the brain. There is increasing evidence that sleep plays an important role in Aβ clearance. Here, we tested our hypothesis that PS at night can stimulate Aβ clearance from the brain more effectively than PS during the day. Our results on healthy mice show that Aβ clearance from the brain occurs faster at night than during wakefulness. The PS course at night improves memory and reduces Aβ accumulation in the brain of AD mice more effectively than the PS course during the day. Our results suggest that night PS is a more promising candidate as an effective method in preve...
This paper presents a novel approach for analyzing the structural properties of time series from ... more This paper presents a novel approach for analyzing the structural properties of time series from realworld complex systems by means of evolving complex networks. Starting from the concept of recurrences in phase space, the recurrence matrices corresponding to different parts of a time series are re-interpreted as the adjacency matrices of complex networks, which link different observations if the associated temporal evolution is sufficiently similar. We provide some illustrative examples demonstrating that the local properties of the resulting recurrence networks allow identifying dynamically invariant objects in the phase space of complex systems. Moreover, changes in the global network properties of evolving recurrence networks allow identifying time intervals containing hidden dynamical transitions, which is exemplified for some financial time series.
The asymptotic behaviour of dynamical processes in networks can be expressed as a function of spe... more The asymptotic behaviour of dynamical processes in networks can be expressed as a function of spectral properties of the Adjacency and Laplacian matrices. Although many theoretical results are known for the spectra of traditional configuration models, networks generated through these models fail to describe many topological features of real-world networks, in particular non-null values for the clustering coefficient. Here we study the effects of cycles or order three (triangles) in network spectra. By using recent advances in random matrix theory, we determine the spectrum distribution of the network Adjacency matrix as a function of the average number of triangles attached to each node for networks without modular structure and degree-degree correlations. Furthermore we show that cycles of order three have a weak influence on the Laplacian eigenvalues, fact that explains the recent controversy on the dynamics of clustered networks. Our findings can shed light in the study of how pa...
2020 and 2021 have been unprecedented years due to the rapid spread of the modified severe acute ... more 2020 and 2021 have been unprecedented years due to the rapid spread of the modified severe acute respiratory syndrome coronavirus around the world. The coronavirus disease 2019 (COVID-19) causes atypical infiltrated pneumonia with many neurological symptoms, and major sleep changes. The exposure of people to stress, such as social confinement and changes in daily routines, is accompanied by various sleep disturbances, known as ‘coronasomnia’ phenomenon. Sleep disorders induce neuroinflammation, which promotes the blood–brain barrier (BBB) disruption and entry of antigens and inflammatory factors into the brain. Here, we review findings and trends in sleep research in 2020–2021, demonstrating how COVID-19 and sleep disorders can induce BBB leakage via neuroinflammation, which might contribute to the ‘coronasomnia’ phenomenon. The new studies suggest that the control of sleep hygiene and quality should be incorporated into the rehabilitation of COVID-19 patients. We also discuss persp...
IEEE Journal of Selected Topics in Quantum Electronics, 2021
In this review, we discuss the crucial role of cranial and the extracranial lymphatics in keeping... more In this review, we discuss the crucial role of cranial and the extracranial lymphatics in keeping the central nervous system (CNS) health. We talk about the important lymphatic mechanism of removal of metabolites and toxins from the brain, which orchestrates the regenerative processes in CNS. We debate a novel knowledge about the lymphatic mechanism responsible for maintaining the balance between the exit and the entrance of Manuscript
Cerebral small vessel disease (CSVD) is a leading cause of cognitive decline in elderly people an... more Cerebral small vessel disease (CSVD) is a leading cause of cognitive decline in elderly people and development of Alzheimer’s disease (AD). Blood–brain barrier (BBB) leakage is a key pathophysiological mechanism of amyloidal CSVD. Sleep plays a crucial role in keeping health of the central nervous system and in resistance to CSVD. The deficit of sleep contributes to accumulation of metabolites and toxins such as beta-amyloid in the brain and can lead to BBB disruption. Currently, sleep is considered as an important informative platform for diagnosis and therapy of AD. However, there are no effective methods for extracting of diagnostic information from sleep characteristics. In this review, we show strong evidence that slow wave activity (SWA) (0–0.5 Hz) during deep sleep reflects glymphatic pathology, the BBB leakage and memory deficit in AD. We also discuss that diagnostic and therapeutic targeting of SWA in AD might lead to be a novel era in effective therapy of AD. Moreover, we ...
IEEE transactions on neural networks and learning systems, 2012
In this paper, a new control strategy is proposed for the synchronization of stochastic dynamical... more In this paper, a new control strategy is proposed for the synchronization of stochastic dynamical networks with nonlinear coupling. Pinning state feedback controllers have been proved to be effective for synchronization control of state-coupled dynamical networks. We will show that pinning impulsive controllers are also effective for synchronization control of the above mentioned dynamical networks. Some generic mean square stability criteria are derived in terms of algebraic conditions, which guarantee that the whole state-coupled dynamical network can be forced to some desired trajectory by placing impulsive controllers on a small fraction of nodes. An effective method is given to select the nodes which should be controlled at each impulsive constants. The proportion of the controlled nodes guaranteeing the stability is explicitly obtained, and the synchronization region is also derived and clearly plotted. Numerical simulations are exploited to demonstrate the effectiveness of th...
Physical review. E, Statistical, nonlinear, and soft matter physics, 2009
Stability of synchronization in unidirectionally coupled time-delay systems is studied using the ... more Stability of synchronization in unidirectionally coupled time-delay systems is studied using the Krasovskii-Lyapunov theory. We have shown that the same general stability condition is valid for different cases, even for the general situation (but with a constraint) where all the coefficients of the error equation corresponding to the synchronization manifold are time dependent. These analytical results are also confirmed by the numerical simulation of paradigmatic examples.
The effect of stirring in an inhomogeneous oscillatory medium is investigated. We show that the s... more The effect of stirring in an inhomogeneous oscillatory medium is investigated. We show that the stirring rate can control the macroscopic behavior of the system producing collective oscillations (synchronization) or complete quenching of the oscillations (oscillator death). We interpret the homogenization rate due to mixing as a measure of global coupling and compare the phase diagrams of stirred oscillatory media and of populations of globally coupled oscillators.
Though the notion of phase synchronization has been well studied in chaotic dynamical systems wit... more Though the notion of phase synchronization has been well studied in chaotic dynamical systems without delay, it has not been realized yet in chaotic time-delay systems exhibiting non-phase coherent hyperchaotic attractors. In this article we report the first identification of phase synchronization in coupled time-delay systems exhibiting hyperchaotic attractor. We show that there is a transition from non-synchronized behavior to phase and then to generalized synchronization as a function of coupling strength. These transitions are characterized by recurrence quantification analysis, by phase differences based on a new transformation of the attractors and also by the changes in the Lyapunov exponents. We have found these transitions in coupled piece-wise linear and in Mackey-Glass time-delay systems.
We report the identification of global phase synchronization (GPS) in a linear array of unidirect... more We report the identification of global phase synchronization (GPS) in a linear array of unidirectionally coupled Mackey-Glass time-delay systems exhibiting highly non-phase-coherent chaotic attractors with complex topological structure. In particular, we show that the dynamical organization of all the coupled time-delay systems in the array to form GPS is achieved by sequential synchronization as a function of the coupling strength. Further, the asynchronous ones in the array with respect to the main sequentially synchronized cluster organize themselves to form clusters before they achieve synchronization with the main cluster. We have confirmed these results by estimating instantaneous phases including phase difference, average phase, average frequency, frequency ratio and their differences from suitably transformed phase coherent attractors after using a nonlinear transformation of the original non-phase-coherent attractors. The results are further corroborated using two other independent approaches based on recurrence analysis and the concept of localized sets from the original non-phase-coherent attractors directly without explicitly introducing the measure of phase.
We study synchronous behavior in ensembles of locally coupled nonidentical Bonhoeffer-van der Pol... more We study synchronous behavior in ensembles of locally coupled nonidentical Bonhoeffer-van der Pol oscillators. We show that, in a chain of N elements not less than 2 N−1 , different coexisting regimes of global synchronization are possible, and we investigate wave-induced synchronous regimes in a chain and in a lattice of coupled nonidentical Bonhoeffer-van der Pol oscillators.
We present an automatic control method for phase locking of regular and chaotic non-identical osc... more We present an automatic control method for phase locking of regular and chaotic non-identical oscillations, when all subsystems interact via feedback. This method is based on the well known principle of feedback control which takes place in nature and is successfully used in engineering. In contrast to unidirectional and bidirectional coupling, our approach supposes the existence of a special controller, whose input is given by a quadratic form of the coordinates of the individual systems and its output is a result of the application of a linear differential operator. Using several examples we demonstrate the effectiveness of our approach to achieve controlled phase synchronization.
This review provides a summary of methods originated in (non-equilibrium) statistical mechanics a... more This review provides a summary of methods originated in (non-equilibrium) statistical mechanics and information theory, which have recently found successful applications to quantitatively studying complexity in various components of the complex Entropy 2013, 15 4845 system Earth. Specifically, we discuss two classes of methods: (i) entropies of different kinds (e.g., on the one hand classical Shannon and Rényi entropies, as well as non-extensive Tsallis entropy based on symbolic dynamics techniques and, on the other hand, approximate entropy, sample entropy and fuzzy entropy); and (ii) measures of statistical interdependence and causality (e.g., mutual information and generalizations thereof, transfer entropy, momentary information transfer). We review a number of applications and case studies utilizing the above-mentioned methodological approaches for studying contemporary problems in some exemplary fields of the Earth sciences, highlighting the potentials of different techniques.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2008
The notion of phase synchronization in time-delay systems, exhibiting highly non-phase-coherent a... more The notion of phase synchronization in time-delay systems, exhibiting highly non-phase-coherent attractors, has not been realized yet even though it has been well studied in chaotic dynamical systems without delay. We report the identification of phase synchronization in coupled nonidentical piecewise linear and in coupled Mackey–Glass time-delay systems with highly non-phase-coherent regimes. We show that there is a transition from nonsynchronized behavior to phase and then to generalized synchronization as a function of coupling strength. We have introduced a transformation to capture the phase of the non-phase-coherent attractors, which works equally well for both the time-delay systems. The instantaneous phases of the above coupled systems calculated from the transformed attractors satisfy both the phase and mean frequency locking conditions. These transitions are also characterized in terms of recurrence-based indices, namely generalized autocorrelation function P(t), correlati...
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2009
Transitions between inverse anticipatory, inverse complete, and inverse lag synchronizations are ... more Transitions between inverse anticipatory, inverse complete, and inverse lag synchronizations are shown to occur as a function of the coupling delay in unidirectionally coupled time-delay systems with inhibitory coupling. We have also shown that the same general asymptotic stability condition obtained using the Krasovskii–Lyapunov functional theory can be valid for the cases where (i) both the coefficients of the Δ(t) (error variable) and Δτ=Δ(t−τ) (error variable with delay) terms in the error equation corresponding to the synchronization manifold are time independent and (ii) the coefficient of the Δ term is time independent, while that of the Δτ term is time dependent. The existence of different kinds of synchronization is corroborated using similarity function, probability of synchronization, and also from changes in the spectrum of Lyapunov exponents of the coupled time-delay systems.
Chaos: An Interdisciplinary Journal of Nonlinear Science, 2004
In the last decade, there has been an increasing interest in compensating thermally induced error... more In the last decade, there has been an increasing interest in compensating thermally induced errors to improve the manufacturing accuracy of modular tool systems. These modular tool systems are interfaces between spindle and workpiece and consist of several complicatedly formed parts. Their thermal behavior is dominated by nonlinearities, delay and hysteresis effects even in tools with simpler geometry and it is difficult to describe it theoretically. Due to the dominant nonlinear nature of this behavior the so far used linear regression between the temperatures and the displacements is insufficient. Therefore, in this study we test the hypothesis whether we can reliably predict such thermal displacements via nonlinear temperature-displacement regression functions. These functions are estimated first from learning measurements using the alternating conditional expectation (ACE) algorithm and then tested on independent data sets. First, we analyze data that were generated by a finite ...
We present recently introduced new recurrence plot based measures of complexity and illustrate th... more We present recently introduced new recurrence plot based measures of complexity and illustrate their potential with applications to the logistic map and heart rate variability data. These new measures make the identification of chaos-chaos transitions possible and identify laminar states. The application to the heart rate variability data detects and quantifies the laminar phases before a lifethreatening cardiac arrhythmia occurs; thereby facilitating a prediction of such an event.
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Papers by Jurgen Kurths