Superextreme spiking oscillations and multistability in a memristor-based Hindmarsh–Rose neuron model

Abstract

In this paper, we investigate the occurrence of superextreme spiking (SES) oscillations and multistability behavior in a memristor-based Hindmarsh–Rose neuron model. The presence of SES oscillations has been identified as arising due to the occurrence of an interior crisis. As the membrane current I(t), considered as the control parameter is varied, the system transits from bounded chaotic spiking (BCS) oscillations to SES oscillations. These transitions are captured numerically using geometrical representations like time series plots, phase portraits and inter-spikes interval return maps. The characterization of SES from the BCS oscillations is made using statistical tools such as phase shift analysis and probability density distribution function. The multistability nature has been observed using bifurcation analysis and confirmed by the Lyapunov exponents for two different sets of initial conditions. The numerical simulations are substantiated through real-time hardware experiments realized through a nonlinear circuit constructed using an analog model of the memristor.