Multistability and synchronicity of memristor coupled adaptive synaptic neuronal network

Abstract

Memristor coupled neuronal networks can simulate the complex interactions between neurons in biological neuronal networks. These capture the current and synaptic transmission between neurons through mathematical equations, thus reflecting the signal transmission and integration in biological neuronal networks. This paper presents a five-dimensional isomorphic memristor coupled adaptive synaptic neuron (mCASN) network using a non-ideal memristor to couple two-dimensional adaptive synaptic neurons. The theoretical analysis of equilibrium points shows that the mCASN network has many different stability types. The complex parameters-dependent bifurcation behaviors are studied using various numerical methods, and the initial state-dependent coexistence behaviors and the riddled-like basins of attraction sensitive to initial states are further revealed, which proves that the coupled network has multistability. In addition, using the normalized average synchronization error method, we reveal that the mCASN network has synchronization characteristics controlled by parameters and initial states. The complete synchronization and lag synchronization induced by the network parameters, the internal variable of the coupled memristor, and the state variable of the sub-neuron are numerically analyzed. Finally, the mCASN network is implemented using an MCU-based digital hardware platform, and the numerical results are verified.