Amplitude death in systems of coupled oscillators with distributed-delay coupling

Abstract

This paper studies the effects of coupling with distributed delay on the suppression of oscillations in a system of coupled Stuart-Landau oscillators. Conditions for amplitude death are obtained in terms of strength and phase of the coupling, as well as the mean time delay and the width of the delay distribution for uniform and gamma distributions. Analytical results are confirmed by numerical computation of the eigenvalues of the corresponding characteristic equations. These results indicate that larger widths of delay distribution increase the regions of amplitude death in the parameter space. In the case of a uniformly distributed delay kernel, for sufficiently large width of the delay distribution it is possible to achieve amplitude death for an arbitrary value of the average time delay, provided that the coupling strength has a value in the appropriate range. For a gamma distribution of delay, amplitude death is also possible for an arbitrary value of the average time delay, provided that it exceeds a certain value as determined by the coupling phase and the power law of the distribution. The coupling phase has a destabilizing effect and reduces the regions of amplitude death.

15 pages, 7 figures

References in corpus (7)

• Distributed Delays Facilitate Amplitude Death of Coupled Oscillators
• Delayed Feedback Control near Hopf Bifurcation
• Time-delayed feedback in neurosystems
• Synchronizing distant nodes: a universal classification of networks
• Stability and bifurcations in an epidemic model with varying immunity period
• Stabilization of unstable steady states by variable delay feedback control
• Variable-delay feedback control of unstable steady states in retarded time-delayed systems

Cited by in corpus (18)

• Time delay control of symmetry-breaking primary and secondary oscillation death
• Amplitude and phase dynamics in oscillators with distributed-delay coupling
• Amplitude death in oscillator networks with variable-delay coupling
• Synchronization of networks of oscillators with distributed delay coupling
• Synchronization of coupled neural oscillators with heterogeneous delays
• Time-delayed models of gene regulatory networks
• Heterogeneous Delays in Neural Networks
• Delayed feedback control of unstable steady states with high-frequency modulation of the delay
• Synchronization-Desynchronization Transitions in Complex Networks: An Interplay of Distributed Time Delay and Inhibitory Nodes
• Aging transition in systems of oscillators with global distributed-delay coupling
• Role of coupling delay in oscillatory activity in autonomous networks of excitable neurons with dissipation
• Synchronization of organ pipes
• Enhancing noise-induced switching times in systems with distributed delays
• Time-delayed model of RNA interference
• Resurgence of oscillation in coupled oscillators under delayed cyclic interaction
• Measure Control of a Semilinear Parabolic Equation with a Nonlocal Time Delay
• Optimal time delays in a class of reaction-diffusion equations
• Symmetry breaking in a model of antigenic variation with immune delay