Route to chaos and chimera states in a network of memristive Hindmarsh-Rose neurons model with external excitation

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