On the limit cycle of a Belousov–Zhabotinsky differential systems

Abstract

In Leonov and Kuznetsov (2013), the authors shown numerically the existence of a limit cycle surrounding the unstable node that system (1) has in the positive quadrant for specific values of the parameters. System (1) is one of the Belousov–Zhabotinsky dynamical models. The objective of this paper is to prove that system (1), when in the positive quadrant Q has an unstable node or focus, has at least one limit cycle, and when , , and ϵ > 0 sufficiently small this limit cycle is unique.