Inverse stochastic resonance in a system of excitable active rotators with adaptive coupling

¹ Scientific Computing Laboratory, Center for the Study of Complex Systems, Institute of Physics Belgrade, University of Belgrade - Pregrevica 118, 11080 Belgrade, Serbia
² Institute of Applied Physics of the Russian Academy of Sciences - 46 Ulyanov Street, 603950 Nizhny Novgorod, Russia
³ Faculty of Natural Sciences and Mathematics, University of Maribor - Koroška cesta 160, SI-2000 Maribor, Slovenia

^(a) franovic@ipb.ac.rs

Received: 17 September 2018
Accepted: 8 November 2018

Abstract

Inverse stochastic resonance is a phenomenon where an oscillating system influenced by noise exhibits a minimal oscillation frequency at an intermediate noise level. We demonstrate a novel generic scenario for such an effect in a multi-timescale system, considering an example of emergent oscillations in two adaptively coupled active rotators with excitable local dynamics. The impact of plasticity turns out to be twofold. First, at the level of multiscale dynamics, one finds a range of intermediate adaptivity rates that give rise to multistability between the limit cycle attractors and the stable equilibria, a condition necessary for the onset of the effect. Second, applying the fast-slow analysis, we show that the plasticity also plays a facilitatory role on a more subtle level, guiding the fast flow dynamics to parameter domains where the stable equilibria become focuses rather than nodes, which effectively enhances the influence of noise. The described scenario persists for different plasticity rules, underlying its robustness in the light of potential applications to neuroscience and other types of cell dynamics.