Non-chaos-mediated mixed-mode oscillations in an extended Hindmarsh-Rose neuronal oscillator with time delay

Abstract

This paper proposes an extended neuron model with time delay. It aims to investigate the effect of time delay on the dynamical behavior of the system under different conditions. The existence of the Hopf bifurcation of the system and the stability of its periodic solution are proved by the central manifold theorem. Numerical results show that the system has abundant dynamical performance, including chaos, period-adding, and intermittent chaos.