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 mul tistability 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), consid ered as the control parameter is varied, the system tran sits from bounded chaotic spiking (BCS) oscillations to SES oscillations. These transitions are captured numer ically using geometrical representations like time series plots, phase portraits and inter-spikes interval return maps. The characterization of SES from the BCS oscil lations is made using statistical tools such as phase shift analysis and probability density distribution function. The multistability nature has been observed using bifur cation analysis and confirmed by the Lyapunonents for two different sets of initial conditions. The numerical simulations are substantiated through real time hardware experiments realized through a nonlin ear circuit constructed using an analog model of the memristor.