Can distributed delays perfectly stabilize dynamical networks?

Abstract

Signal transmission delays tend to destabilize dynamical networks leading to oscillation, but their dispersion contributes oppositely toward stabilization. We analyze an integro-differential equation that describes the collective dynamics of a neural network with distributed signal delays. With the gamma distributed delays less dispersed than exponential distribution, the system exhibits reentrant phenomena, in which the stability is once lost but then recovered as the mean delay is increased. With delays dispersed more highly than exponential, the system never destabilizes.

4pages 5figures

References in corpus (6)

• Time Delay in the Kuramoto Model of Coupled Oscillators
• Distributed Delays Facilitate Amplitude Death of Coupled Oscillators
• Random Delays and the Synchronization of Chaotic Maps
• Cooperative Dynamics in a Network of Stochastic Elements with Delayed Feedback
• Steady-state stabilization due to random delays in maps with self-feedback loops and in globally delayed-coupled maps
• Reverberating activity in a neural network with distributed signal transmission delays

Cited by in corpus (8)

• Amplitude Death: The emergence of stationarity in coupled nonlinear systems
• Amplitude death in oscillator networks with variable-delay coupling
• Synchronizability of chaotic logistic maps in delayed complex networks
• Complex transitions to synchronization in delay-coupled networks of logistic maps
• Statistical multi-moment bifurcations in random delay coupled swarms
• Capturing pattern bi-stability dynamics in delay-coupled swarms
• Randomly Distributed Delayed Communication and Coherent Swarm Patterns
• Noise Induced Pattern Switching in Randomly Distributed Delayed Swarm Patterns