Time Delay Effects on Coupled Limit Cycle Oscillators at Hopf Bifurcation

Abstract

We present a detailed study of the effect of time delay on the collective dynamics of coupled limit cycle oscillators at Hopf bifurcation. For a simple model consisting of just two oscillators with a time delayed coupling, the bifurcation diagram obtained by numerical and analytical solutions shows significant changes in the stability boundaries of the amplitude death, phase locked and incoherent regions. A novel result is the occurrence of amplitude death even in the absence of a frequency mismatch between the two oscillators. Similar results are obtained for an array of N oscillators with a delayed mean field coupling and the regions of such amplitude death in the parameter space of the coupling strength and time delay are quantified. Some general analytic results for the N tending to infinity (thermodynamic) limit are also obtained and the implications of the time delay effects for physical applications are discussed.

20 aps formatted revtex pages (including 13 PS figures); Minor changes over the previous version; To be published in Physica D

References in corpus (1)

• Time Delay Induced Death in Coupled Limit Cycle Oscillators

Cited by in corpus (28)

• Amplitude Death: The emergence of stationarity in coupled nonlinear systems
• Distributed Delays Facilitate Amplitude Death of Coupled Oscillators
• Amplitude death in coupled chaotic oscillators
• Dynamics of FitzHugh-Nagumo excitable systems with delayed coupling
• Phaselocked patterns and amplitude death in a ring of delay coupled limit cycle oscillators
• Total and partial amplitude death in networks of diffusively coupled oscillators
• Dynamics of a Limit Cycle Oscillator under Time Delayed Linear and Nonlinear Feedbacks
• Amplitude and phase dynamics in oscillators with distributed-delay coupling
• Amplitude death in oscillator networks with variable-delay coupling
• Amplitude death in systems of coupled oscillators with distributed-delay coupling
• Transition to amplitude death in scale-free networks
• Amplitude death and synchronized states in nonlinear time-delay systems coupled through mean-field diffusion
• Exceptional points in coupled dissipative dynamical systems
• Aging transition in systems of oscillators with global distributed-delay coupling
• Occasional coupling enhances amplitude death in delay-coupled oscillators
• Synchronization of two coupled multimode oscillators with time-delayed feedback
• Dynamical States and Bifurcations in Coupled Thermoacoustic Oscillators
• Amplitude death in networks of delay-coupled delay oscillators
• Oscillation death in coupled counter-rotating identical nonlinear oscillators
• Amplitude death in a ring of nonidentical nonlinear oscillators with unidirectional coupling
• An approach to normal forms of Kuramoto model with distributed delays and the effect of minimal delay
• Resurgence of oscillation in coupled oscillators under delayed cyclic interaction
• Codimension-two Bifurcations Induce Hysteresis Behavior and Multistabilities in Delay-coupled Kuramoto Oscillators
• Double Hopf bifurcation in delayed reaction-diffusion systems
• Synchronization in a market model with time delays
• Bifurcations due to small time-lag in coupled excitable systems
• Delayed-mutual coupling dynamics of lasers: scaling laws and resonances
• Driven response of time delay coupled limit cycle oscillators