The effects of extreme multistability on the collective dynamics of coupled memristive neurons

The coexistence of different attractors, known as multistability, is an exciting phenomenon in the nonlinear dynamics field. Multistability has been widely studied in different dynamical systems; however, it has received less attention in coupled oscillators. This paper investigates coupled memristive Hindmarsh-Rose neurons, in which the memristor shows the effects of electromagnetic induction. The model has extreme multistability depending on the initial condition of the memristor. The collective behaviors of the network are considered by selecting different sets of initial conditions. The results represent the formation of different chimera, multi-headed chimera, and cluster synchronization patterns. The dynamics of neurons also rely on the coupling strength and may vary in time between the attractors. In periodic firing, the neurons can generate four clusters that have synchronous variations in different amplitudes.