Route to Chaos and Chimera States in a Network of Memristive Hindmarsh-Rose Neurons Model with External Excitation

Authors : Sishu Shankar MUNİ, Zeric NJITACKE, Cyrille FEUDJİO, Théophile FOZİN, Jan AWREJCEWİCZ

Pages : 119-127

Doi:10.51537/chaos.1144123

View : 18 | Download : 6

Publication Date : 2022-11-30

Article Type : Research Paper

Abstract :In this paper we have introduced and investigated the collective behavior of a network of memristive Hindmarsh-Rose insert ignore into journalissuearticles values(HR); neurons. The proposed model was built considering the memristive autapse of the traditional 2D HR neuron. Using the one-parameter bifurcation diagram and its corresponding maximal Lyapunov exponent graph, we showed that the proposed model was able to exhibit a reverse period doubling route to chaos, phenomenon of interior and exterior crises. Three different configurations of the ring-star network of the memristive HR neuron model, including ring-star, ring, and star, have been considered. The study of those network configurations revealed incoherent, coherent , chimera and cluster state behaviors. Coherent behavior is characterized by synchronization of the neurons of the network, while incoherent behaviors are characterized by the absence of synchronization. Chimera states refer to a differet state where there is a coexistence of synchroniaed and asynchronized nodes of the network. One of the interesting result of the paper is the prevalence of double-well chimera states in both ring and ring-star network and has been first mentioned in the case of memrisitve HR neuron model.
Keywords : 2D Hindmarsh Rose neuron, Memristive autapse routes to chaos, Ring star network, Chimera states, Double well chimera state