Dynamic behaviors of a two-neuron model coupled with memristor and its analog circuit implementation

Considering that the synaptic connection weight between two neurons in a neural network is time-dependent, a two-neuron model coupled with one synapse is proposed. Meanwhile, a type of memristor is introduced to reveal the electromagnetic induction effect. Complicated dynamics of the addressed system with system parameters changing are explored via phase portraits, time series, bifurcation diagram and Lyapunov exponents. The phenomenon of coexistence of various attractors, chaos transient as well as chaotic crisis is detected. In addition, the analog circuit implementation is used to simulate the dynamics of the addressed system. Some simulations of output voltages and time waveform are captured. The research results of numerical simulation and analog circuits have potential application for revealing the dynamical behaviors of neural network and designing integrated circuits.