Stochastic control of spiking activity bump expansion: monotonic and resonant phenomena

TL;DR

This paper investigates how multiplicative noise influences the growth and contraction of localized spiking activity patterns, or bumps, in bistable oscillator networks, revealing monotonic and resonant phenomena and the constructive role of nonlocal coupling.

Contribution

It demonstrates the control of bump dynamics through noise modulation and highlights the contrasting monotonic and resonant effects in different oscillator models, emphasizing the importance of nonlocal coupling.

Findings

Noise intensity can control bump expansion and contraction.

Resonant noise effects stabilize activity at specific noise levels.

Nonlocal coupling preserves activity domains against noise destruction.

Abstract

We consider spatially localized spiking activity patterns, so-called bumps, in ensembles of bistable spiking oscillators. The bistability consists in the coexistence of self-sustained spiking dynamics and quiescent steady-state regime. We show numerically that the processes of growth or contraction of such patterns can be controlled by varying the intensity of multiplicative noise. In particular, the effect of the noise is monotonic in an ensemble of the coupled Hindmarsh-Rose oscillators. On the other hand, in another model proposed by V. Semenov et al. in 2016 (see Ref. [V. Semenov et al., Phys. Rev. E 93, 052210 (2016)]), a resonant noise effect is observed. In that model, stabilization of the activity bump expansion is achieved at an appropriate noise level, and the noise effect reverses with a further increase in noise intensity. Moreover, we show the constructive role of nonlocal coupling which allows to save domains and fronts being totally destroyed due to the action of noise in the case of local coupling.