Excitable systems with noise and delay with applications to control: renewal theory approach

Abstract

We present an approach for the analytical treatment of excitable systems with noise-induced dynamics in the presence of time delay. An excitable system is modeled as a bistable system with a time delay, while another delay enters as a control term taken after [Pyragas 1992] as a difference between the current system state and its state "tau" time units before. This approach combines the elements of renewal theory to estimate the essential features of the resulting stochastic process as functions of the parameters of the controlling term.

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Cited by in corpus (6)

• Control of coherence resonance in semiconductor superlattices
• Resonant control of stochastic spatio-temporal dynamics in a tunnel diode by multiple time delayed feedback
• Two Scenarios for the Onset and Suppression of Collective Oscillations in Heterogeneous Populations of Active Rotators
• Persistence and failure of mean-field approximations adapted to a class of systems of delay-coupled excitable units
• Delay-induced stochastic bursting in excitable noisy systems
• Feedback-dependent control of stochastic synchronization in coupled neural systems