A bistable locally active memristor multisynaptically coupled to Rulkov neurons

The study of memristor simulation of neuronal synapses has been more extensive and in-depth. However, the study of simulation of neuronal connectivity structure in the cerebral cortex has not yet attracted people's attention. In this paper, a novel bistable locally active discrete memristor is proposed as a neuronal autosynapse and synapse to simulate the connection structure of neurons in the cerebral cortex. Dynamical methods such as equilibrium point stability, Lyapunov exponential spectrum and bifurcation diagrams are utilized for analytical studies. Numerical simulations reveal that the proposed multisynaptic coupled Rulkov neural network has multiple brain-like firing patterns. Multiple attractor phase diagrams with periodic-periodic, periodic-chaotic, and chaotic-chaotic coexistence as well as high complexity are found. Digital signal processing-based hardware implementation platform was also developed, on which the attractor phase diagrams realized by the simulation platform were experimentally captured. New ideas are provided for the future construction of cerebral cortical neuron models.