Controlling the bursting size in the two-dimensional Rulkov model, XLIII Dynamics Days Europe 2023

Abstract

This paper presents a novel method for controlling the bursting size in the two-dimensional Rulkov model affected by bounded noise. By selecting appropriate parameters, the phase space of this neuronal model exhibits two separated chaotic regions. Typically, the orbits exhibit bursts in one of these chaotic regions where they remain trapped, resulting in short-duration bursts. Our approach involves designing a connecting region between the two chaotic regions, enabling the orbits to exhibit long burst behavior. To achieve this, we propose a control technique that applies tiny controls over the variables when the orbit passes through the connecting region, preserving the chaotic behavior of the bursting. Our method is demonstrated to be effective in controlling bursting size under various noise intensities and scenarios.