Synchronized states in chaotic systems coupled indirectly through a dynamic environment

Abstract

We consider synchronization of chaotic systems coupled indirectly through a common environmnet where the environment has an intrinsic dynmics of its own modulated via feedback from the systems. We find that a rich vareity of synchronization behavior, such as in-phase, anti-phase,complete and anti- synchronization is possible. We present an approximate stability analysis for the different synchronization behaviors. The transitions to different states of synchronous behaviour are analyzed in the parameter plane of coupling strengths by numerical studies for specific cases such as Rossler and Lorenz systems and are characterized using various indices such as correlation, average phase difference and Lyapunov exponents. The threshold condition obtained from numerical analysis is found to agree with that from the stability analysis.

7 pages, 11 figures, appeared in Phys Rev E 81, 046216 (2010)

References in corpus (4)

• Collective Atomic Recoil Laser as a synchronization transition
• Synchronization of oscillators coupled through an environment
• Anticipatory synchronization with variable time delay and reset
• Inverse synchronizations in coupled time-delay systems with inhibitory coupling

Cited by in corpus (20)

• Amplitude Death: The emergence of stationarity in coupled nonlinear systems
• General mechanism for amplitude death in coupled systems
• Global convergence of quorum-sensing networks
• Amplitude death in complex networks induced by environment
• Transitions among the diverse oscillation quenching states induced by the interplay of direct and indirect coupling
• Amplitude death and synchronized states in nonlinear time-delay systems coupled through mean-field diffusion
• Environmental coupling in ecosystems: From oscillation quenching to rhythmogenesis
• Synchronization in hyperchaotic time-delayed electronic oscillators coupled indirectly via a common environment
• Phase-flip chimera induced by environmental nonlocal coupling
• Different Types of Synchronization in Coupled Network Based Chaotic Circuits
• Chimera at the phase-flip transition of an ensemble of identical nonlinear oscillators
• Dynamic environment coupling induce synchronized states in coupled time-delayed electronic circuits
• Quorum sensing in populations of spatially extended chaotic oscillators coupled indirectly via a heterogeneous environment
• Revisiting linear augmentation for stabilizing stationary solutions: potential pitfalls and their application
• Tipping induced by multiplexing on two layer networks
• Synchronization of active rotators interacting with environment
• Mixed mode oscillation suppression states in coupled oscillators
• Collective behavior of chaotic oscillators with environmental coupling
• Neuronal networks with coupling through amyloid beta: towards a theory for Alzheimer's disease
• The role of intermediaries in the synchronization of pulse-coupled oscillators