Synchronization transitions caused by time-varying coupling functions

Abstract

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’.

Time Window Determination for Inference of Time-Varying Dynamics: Application to Cardiorespiratory Interaction

“…Different aspects of the cardiorespiratory interaction have been studied, including phase synchronization, coupling strength/directionality and the coupling functions (Rosenblum et al, 2002;Paluš and Stefanovska, 2003;Voss et al, 2008;Stankovski et al, 2012;Kralemann et al, 2013a;Hagos et al, 2019). The latter describe the functional mechanism of how the interactions occur and develop (Stankovski et al, 2017).…”

Time‐evolving coupling functions for evaluating the interaction between cerebral oxyhemoglobin and arterial blood pressure with hypertension

“…The DBI of the coupling functions was used to reconstruct a stochastic differential model, where the deterministic part was allowed to be time varying 20,21,50 . The model to be inferred is described by the following stochastic differential equation: 51 where is the parameter of the natural frequency, and is the phase of oscillator . The coupling function describes the influence of oscillator on the phase of oscillator .…”

False Asymptotic Instability Behavior at Iterated Functions with Lyapunov Stability in Nonlinear Time Series

“…Note that this same results approximation can be seen at Monte Carlo calculations, but differing in terms of finding how the mathematical expectation of the not i.i.d. complex variables iterations and interactions of 𝑔(𝑥) might express as outcomes towards time and system own coupling functions dynamics [26], and thus not defining any visible weight to the probabilistic distributions oscillations (visible by a central limit theorem). This approach is, for example, different from the Tang [27] framework, that identifies weights and the correlation of the system with the central limit theorem, thus resembling the uniqueness concept of stability.…”

“…Also, this interactive system and probabilistic distributions share not only physical components within the coupling relations, but there are biological agents [26,28] that causes in many distinct aspects, influences over system functioning. In the view of modern scientific breakthrough, analyzing nonlinearity in the light of public administrative policy and infrastructure [29] are demands of investigations that can constitute a path to establish complex solutions for social systems that present nowadays high level of non-convergence and artificial oscillatory dynamics.…”