scholarly journals Synchronization transitions caused by time-varying coupling functions

2019 ◽  
Vol 377 (2160) ◽  
pp. 20190275 ◽  
Author(s):  
Zeray Hagos ◽  
Tomislav Stankovski ◽  
Julian Newman ◽  
Tiago Pereira ◽  
Peter V. E. McClintock ◽  
...  
Keyword(s):  
Social Sciences ◽  
Dynamical Systems ◽  
Coupling Strength ◽  
Phase Synchronization ◽  
Time Variable ◽  
Time Variability ◽  
Time Varying ◽  
Theme Issue ◽  
Dynamical Interaction ◽  
Variable Coupling

Interacting dynamical systems are widespread in nature. The influence that one such system exerts on another is described by a coupling function; and the coupling functions extracted from the time-series of interacting dynamical systems are often found to be time-varying. Although much effort has been devoted to the analysis of coupling functions, the influence of time-variability on the associated dynamics remains largely unexplored. Motivated especially by coupling functions in biology, including the cardiorespiratory and neural delta-alpha coupling functions, this paper offers a contribution to the understanding of effects due to time-varying interactions. Through both numerics and mathematically rigorous theoretical consideration, we show that for time-variable coupling functions with time-independent net coupling strength, transitions into and out of phase- synchronization can occur, even though the frozen coupling functions determine phase-synchronization solely by virtue of their net coupling strength. Thus the information about interactions provided by the shape of coupling functions plays a greater role in determining behaviour when these coupling functions are time-variable. This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences’.

scholarly journals Recent advances in coupled oscillator theory

2019 ◽  
Vol 377 (2160) ◽  
pp. 20190092 ◽  
Author(s):  
Bard Ermentrout ◽  
Youngmin Park ◽  
Dan Wilson
Keyword(s):  
Social Sciences ◽  
Coupled Oscillators ◽  
Weak Coupling ◽  
Standard Theory ◽  
Theme Issue ◽  
Coupled Oscillator ◽  
Dynamical Interaction ◽  
Weakly Coupled ◽  
The Stability ◽  
Oscillator Theory

We review the theory of weakly coupled oscillators for smooth systems. We then examine situations where application of the standard theory falls short and illustrate how it can be extended. Specific examples are given to non-smooth systems with applications to the Izhikevich neuron. We then introduce the idea of isostable reduction to explore behaviours that the weak coupling paradigm cannot explain. In an additional example, we show how bifurcations that change the stability of phase-locked solutions in a pair of identical coupled neurons can be understood using the notion of isostable reduction. This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences’.

scholarly journals Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences

2019 ◽  
Vol 377 (2160) ◽  
pp. 20190039 ◽  
Author(s):  
Tomislav Stankovski ◽  
Tiago Pereira ◽  
Peter V. E. McClintock ◽  
Aneta Stefanovska
Keyword(s):  
Social Sciences ◽  
Social Science ◽  
Respiratory Physiology ◽  
Theme Issue ◽  
Dynamical Interaction ◽  
Future Evolution ◽  
Interaction Mechanisms ◽  
Recent Developments ◽  
Functional Mechanisms ◽  
Breaking Work

Dynamical systems are widespread, with examples in physics, chemistry, biology, population dynamics, communications, climatology and social science. They are rarely isolated but generally interact with each other. These interactions can be characterized by coupling functions—which contain detailed information about the functional mechanisms underlying the interactions and prescribe the physical rule specifying how each interaction occurs. Coupling functions can be used, not only to understand, but also to control and predict the outcome of the interactions. This theme issue assembles ground-breaking work on coupling functions by leading scientists. After overviewing the field and describing recent advances in the theory, it discusses novel methods for the detection and reconstruction of coupling functions from measured data. It then presents applications in chemistry, neuroscience, cardio-respiratory physiology, climate, electrical engineering and social science. Taken together, the collection summarizes earlier work on coupling functions, reviews recent developments, presents the state of the art, and looks forward to guide the future evolution of the field. This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences’.

scholarly journals Dynamical disentanglement in an analysis of oscillatory systems: an application to respiratory sinus arrhythmia

2019 ◽  
Vol 377 (2160) ◽  
pp. 20190045 ◽  
Author(s):  
M. Rosenblum ◽  
M. Frühwirth ◽  
M. Moser ◽  
A. Pikovsky
Keyword(s):  
Social Sciences ◽  
Heart Rate ◽  
Multivariate Data Analysis ◽  
Dynamics Model ◽  
Theme Issue ◽  
Sinus Arrhythmia ◽  
Dynamical Interaction ◽  
Phase Dynamics ◽  
Bivariate Data ◽  
Oscillatory Systems

We develop a technique for the multivariate data analysis of perturbed self-sustained oscillators. The approach is based on the reconstruction of the phase dynamics model from observations and on a subsequent exploration of this model. For the system, driven by several inputs, we suggest a dynamical disentanglement procedure, allowing us to reconstruct the variability of the system's output that is due to a particular observed input, or, alternatively, to reconstruct the variability which is caused by all the inputs except for the observed one. We focus on the application of the method to the vagal component of the heart rate variability caused by a respiratory influence. We develop an algorithm that extracts purely respiratory-related variability, using a respiratory trace and times of R-peaks in the electrocardiogram. The algorithm can be applied to other systems where the observed bivariate data can be represented as a point process and a slow continuous signal, e.g. for the analysis of neuronal spiking. This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences’.

scholarly journals State-dependent effective interactions in oscillator networks through coupling functions with dead zones

2019 ◽  
Vol 377 (2160) ◽  
pp. 20190042 ◽  
Author(s):  
Peter Ashwin ◽  
Christian Bick ◽  
Camille Poignard
Keyword(s):  
Social Sciences ◽  
Effective Interaction ◽  
Structural Connectivity ◽  
Effective Coupling ◽  
Theme Issue ◽  
Dynamical Interaction ◽  
Effective Interactions ◽  
Dead Zones ◽  
Oscillator Networks ◽  
State Dependent

The dynamics of networks of interacting dynamical systems depend on the nature of the coupling between individual units. We explore networks of oscillatory units with coupling functions that have ‘dead zones’, that is the coupling functions are zero on sets with interior. For such networks, it is convenient to look at the effective interactions between units rather than the (fixed) structural connectivity to understand the network dynamics. For example, oscillators may effectively decouple in particular phase configurations. Along trajectories, the effective interactions are not necessarily static, but the effective coupling may evolve in time. Here, we formalize the concepts of dead zones and effective interactions. We elucidate how the coupling function shapes the possible effective interaction schemes and how they evolve in time. This article is part of the theme issue ‘Coupling functions: dynamical interaction mechanisms in the physical, biological and social sciences’.

Complex projection synchronization of fractional order uncertain complex-valued networks with time-varying coupling

2019 ◽  
Vol 33 (29) ◽  
pp. 1950351 ◽  
Author(s):  
Dawei Ding ◽  
Xiaolei Yao ◽  
Hongwei Zhang
Keyword(s):  
Fractional Order ◽  
Coupling Strength ◽  
Dynamic Networks ◽  
Sufficient Conditions ◽  
Feedback Gain ◽  
Time Varying ◽  
Order Complex ◽  
Unknown Parameters ◽  
Synchronization Problem ◽  
Complex Valued

In this paper, the complex projection synchronization problem of fractional complex-valued dynamic networks is investigated. Considering the time-varying coupling and unknown parameters of the fractional order complex network, several decentralized adaptive strategies are designed to adjust the coupling strength and controller feedback gain in order to investigate the complex projection synchronization problem of the system. Moreover, based on the designed identification law, the uncertain parameters in the network can be estimated. Using adaptive law which balances the time-varying coupling strength and the feedback gain of the controller, some sufficient conditions are obtained for the complex projection synchronization of complex networks. Finally, numerical simulation examples are provided to illustrate the efficiency of the complex projection synchronization strategies of the fractional order complex dynamic networks.

scholarly journals Phase Synchronization Is the Amplified Result by the Hilbert Transform

2015 ◽  
Vol 2015 ◽  
pp. 1-3 ◽  
Author(s):  
Ming-Chi Lu ◽  
Hsing-Chung Ho ◽  
Chen-An Chan ◽  
Chia-Ju Liu ◽  
Jiann-Shing Lih ◽  
...  
Keyword(s):  
Time Series ◽  
Dynamical Systems ◽  
Hilbert Transform ◽  
Phase Synchronization ◽  
Nonlinear Dynamical Systems ◽  
The State ◽  
Nonlinear Dynamical ◽  
Large Correlation ◽  
Current Usage ◽  
The Hilbert Transform

We investigate the interplay between phase synchronization and amplitude synchronization in nonlinear dynamical systems. It is numerically found that phase synchronization intends to be established earlier than amplitude synchronization. Nevertheless, amplitude synchronization (or the state with large correlation between the amplitudes) is crucial for the maintenance of a high correlation between two time series. A breakdown of high correlation in amplitudes will lead to a desynchronization of two time series. It is shown that these unique features are caused essentially by the Hilbert transform. This leads to a deep concern and criticism on the current usage of phase synchronization.

GENERALIZED SYNCHRONIZATION, FREQUENCY-LOCKING AND PHASE-LOCKING OF COUPLED SINE CIRCLE MAPS

2001 ◽  
Vol 11 (08) ◽  
pp. 2245-2253
Author(s):  
WEN-XIN QIN
Keyword(s):  
Dynamical Systems ◽  
Invariant Manifold ◽  
Coupling Strength ◽  
Phase Locking ◽  
Coupled System ◽  
Generalized Synchronization ◽  
Frequency Locking ◽  
Local Systems ◽  
Circle Maps ◽  
The Individual

Applying invariant manifold theorem, we study the existence of generalized synchronization of a coupled system, with local systems being different sine circle maps. We specify a range of parameters for which the coupled system achieves generalized synchronization. We also investigate the relation between generalized synchronization, predictability and equivalence of dynamical systems. If the parameters are restricted in the specified range, then all the subsystems are topologically equivalent, and each subsystem is predictable from any other subsystem. Moreover, these subsystems are frequency locked even if the frequencies are greatly different in the absence of coupling. If the local systems are identical without coupling, then the widths of the phase-locked intervals of the coupled system are the same as those of the individual map and are independent of the coupling strength.

scholarly journals New applications of the renormalization group method in physics: a brief introduction

2011 ◽  
Vol 369 (1946) ◽  
pp. 2602-2611 ◽  
Author(s):  
Y. Meurice ◽  
R. Perry ◽  
S.-W. Tsai
Keyword(s):  
Renormalization Group ◽  
Phase Transitions ◽  
Dynamical Systems ◽  
Particle Physics ◽  
Recent Progress ◽  
Condensed Matter ◽  
Group Method ◽  
Renormalization Group Method ◽  
Theme Issue ◽  
New Applications

The renormalization group (RG) method developed by Ken Wilson more than four decades ago has revolutionized the way we think about problems involving a broad range of energy scales such as phase transitions, turbulence, continuum limits and bifurcations in dynamical systems. The Theme Issue provides articles reviewing recent progress made using the RG method in atomic, condensed matter, nuclear and particle physics. In the following, we introduce these articles in a way that emphasizes common themes and the universal aspects of the method.

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