Action potential and chaos near the edge of chaos in memristive circuits

Memristor-based neuromorphic systems have a neuro-bionic function, which is critical for possibly overcoming Moore's law limitation and the von Neumann bottleneck problem. To explore neural behaviors and complexity mechanisms in memristive circuits, this paper proposes an N-type locally active memristor, based on which a third-order memristive circuit is constructed. Theoretical analysis shows that the memristive circuit can exhibit not only various action potentials but also self-sustained oscillation and chaos. Based on Chua's theory of local activity, this paper finds that the neural behaviors and chaos emerge near the edge of chaos through subcritical Hopf bifurcation, in which the small unstable limit cycle is depicted by the dividing line between the attraction basin of the large stable limit cycle and the attraction basin of the stable equilibrium point. Furthermore, an analog circuit is designed to imitate the action potentials and chaos, and the simulation results are in agreement with the theoretical analysis.