Chimeralike states in networks of bistable time-delayed feedback oscillators coupled via the mean field (original) (raw)

Collective dynamics of delay-coupled limit cycle oscillators

Pramana-journal of Physics, 2005

Coupled limit cycle oscillators with instantaneous mutual coupling offer a useful but idealized mathematical paradigm for the study of collective behavior in a wide variety of biological, physical and chemical systems. In most real-life systems however the interaction is not instantaneous but is delayed due to finite propagation times of signals, reaction times of chemicals, individual neuron firing periods in neural networks etc. We present a brief overview of the effect of time-delayed coupling on the collective dynamics of such coupled systems. Simple model equations describing two oscillators with a discrete time-delayed coupling as well as those describing linear arrays of a large number of oscillators with time-delayed global or local couplings are studied. Analytic and numerical results pertaining to time delay induced changes in the onset and stability of amplitude death and phase-locked states are discussed. A number of recent experimental and theoretical studies reveal interesting new directions of research in this field and suggest exciting future areas of exploration and applications.

Emergent dynamics in delayed coupled networks

arXiv: Adaptation and Self-Organizing Systems, 2019

We investigate different emergent dynamics namely oscillation quenching and revival of oscillation in a global network of identical oscillators coupled with diffusive (positive) delay coupling as it is perturbed by symmetry breaking localized repulsive delayed interaction. Starting from the oscillatory states (OS) we systematically identify three types of transition phenomena in the parameter space: (1) The system may reach inhomogeneous steady states (IHSS) from the homogeneous steady state (HSS) sometimes called as the transition from amplitude death (AD) to oscillation death (OD) state i.e. OS-AD-OD scenario, (2) Revival of oscillation (OS) from the AD state (OS-AD-OS) and (3) Emergence of OD state from oscillatory state (OS) without passing through AD i.e. OS-OD. The dynamics of each node in the network is assumed to be governed either by identical limit cycle Stuart-Landau system or by chaotic Rossler system. Based on clustering behavior observed in oscillatory network we deriv...

Stability and Resonance in Networks of Delay-Coupled Delay Oscillators

2010

Dynamical networks with time delays can pose a considerable challenge for mathematical analysis. Here, we extend the approach of generalized modeling to investigate the stability of large networks of delay-coupled delay oscillators. When the local dynamical stability of the network is plotted as a function of the two delays then a pattern of tongues is revealed. Exploiting a link between structure and dynamics, we identify conditions under which perturbations of the topology have a strong impact on the stability. If these critical regions are avoided the local stability of large random networks can be well approximated analytically.

Seaching heteroclinic orbits in time-delayed fully-connected oscillators networks

2015

Connecting orbits in oscillator networks have been well studied for the case of ideal transport delay between nodes and for weakly connected networks. This kind of behavior can emerge either as natural consequence of the network symmetry, appearing as symmetry-breaking bifurcations from equilibria; or in asymmetric networks as a global dynamics. The influence of the transport delay between oscillators in this kind of dynamics has been also studied for the case of scalar oscillators. In Symmetric bifurcation analysis of synchronous states of time-delayed coupled Phase-Locked Loop oscillators. Communications in Nonlinear Science and Numerical Simulation, Elsevier BV, 2014, (on-line version), we presented an analysis of bifurcations in time-delay fully-connected second-order PLL networks focusing in bifurcations from the stable equilibria; in this work we continue the analysis, this time looking for heteroclinic orbits at the linearization for unstable equilibria. We begin to explore t...

Synchronization effects in networks of stochastic bistable oscillators

Mathematics and Computers in Simulation, 2002

We study the collective dynamics of one-and two-dimensional lattices of coupled stochastic, non-homogeneous oscillators in terms of synchronization. This phenomenon manifests itself as an entrainment of the mean switching frequencies in the form of frequency-locking and frozen synchronized states and as in-or anti-phase hopping dynamics. We analyze the conditions for the onset and existence of these different behavioral regimes.

Distributed delays in systems of coupled phase oscillators

2012

We study systems of identical coupled oscillators introducing a distribution of delay times in the coupling. For arbitrary network topologies, we show that the frequency and stability of the fully synchronized states depend only on the mean of the delay distribution. However, synchronization dynamics is sensitive to the shape of the distribution. In the presence of coupling delays, the synchronization rate can be maximal for a specific value of the coupling strength.

Bistable solutions in the onset of the synchronization of a array of oscillators

The existence of multi-stable solutions in the onset of synchronization of the lckm has been investigated in recent years by **, in what the topology of the system proved to be tantamount of existence/non-existence of multistable solutions.In our paper we investigated a array of oscillators synchronized with external forces, we show that this systems presents bi-stability, we deduce analitical expressions for symmetrical cases.

Emergent dynamics in delayed attractive-repulsively coupled networks

Chaos: An Interdisciplinary Journal of Nonlinear Science

We investigate different emergent dynamics namely oscillation quenching and revival of oscillation in a global network of identical oscillators coupled with diffusive (positive) delay coupling as it is perturbed by symmetry breaking localized repulsive delayed interaction. Starting from the oscillatory states (OS) we systematically identify three types of transition phenomena in the parameter space: (1) The system may reach inhomogeneous steady states (IHSS) from the homogeneous steady state (HSS) sometimes called as the transition from amplitude death (AD) to oscillation death (OD) state i.e. OS-AD-OD scenario, (2) Revival of oscillation (OS) from the AD state (OS-AD-OS) and (3) Emergence of OD state from oscillatory state (OS) without passing through AD i.e. OS-OD. The dynamics of each node in the network is assumed to be governed either by identical limit cycle Stuart-Landau system or by chaotic Rössler system. Based on clustering behavior observed in oscillatory network we derive a reduced low-dimensional model of the large network. Using the reduced model, we investigate the effect of time delay on these transitions and demarcate OS, AD and OD regimes in the parameter space. We also explore and characterize the bifurcation transitions present in both systems. The generic behavior of the low dimensional model and full network are found to match satisfactorily.