Complex dynamic behaviors in hyperbolic-type memristor-based cellular neural network

Abstract

This paper presents a new hyperbolic-type memristor model, whose frequency-dependent pinched hysteresis loops and equivalent circuit are tested by numerical simulations and analog integrated operational amplifier circuits. Based on the hyperbolic-type memristor model, we design a cellular neural network (CNN) with 3-neurons, whose characteristics are analyzed by bifurcations, basins of attraction, complexity analysis, and circuit simulations. We find that the memristive CNN can exhibit some complex dynamic behaviors, including multi-equilibrium points, state-dependent bifurcations, various coexisting chaotic and periodic attractors, and offset of the positions of attractors. By calculating the complexity of the memristor-based CNN system through the spectral entropy (SE) analysis, it can be seen that the complexity curve is consistent with the Lyapunov exponent spectrum, i.e., when the system is in the chaotic state, its SE complexity is higher, while when the system is in the periodic state, its SE complexity is lower. Finally, the realizability and chaotic characteristics of the memristive CNN system are verified by an analog circuit simulation experiment.