c © World Scientific Publishing Company DOI: 10.1142/S021812741430016X Cellular Memristive Dynamical Systems (CMDS)

This study presents a cellular-based mapping for a special class of dynamical systems for embed-ding neuron models, by exploiting an efficient memristor crossbar-based circuit for its implemen-tation. The resultant reconfigurable memristive dynamical circuit exhibits various bifurcation phenomena, and responses that are characteristic of dynamical systems. High programmability of the circuit enables it to be applied to real-time applications, learning systems, and analyt-ically indescribable dynamical systems. Moreover, its efficient implementation platform makes it an appropriate choice for on-chip applications and prostheses. We apply this method to the Izhikevich, and FitzHugh–Nagumo neuron models as case studies, and investigate the dynamical behaviors of these circuits