Boundary dynamics of a non-smooth memristive Hindmarsh–Rose neuron system

Abstract

In this paper, the complex dynamics of non-smooth Hindmarsh–Rose (HR) neuron system with local active memristors is discussed through the theory of discontinuous dynamical system. Six mapping structures through two boundaries are employed to illustrate the various switching behaviors of the system. The analytical conditions of the HR system for the switching motions, such as passable motion and grazing motion, are investigated, and the extreme multistability of the improved HR neuron is revealed through switching bifurcations, parameter maps, and attraction basins. The firing activities of various modes in the HR system and the coexistence of various firing behaviors are observed by changing the initial values. Furthermore, the hardware circuit implement of the HR system is established to validate the numerical results.