Abstract
The memristor-based FitzHugh-Nagumo neuron system shows special dynamical behaviors, which make it have a good application in the fields of image processing and signal transmission. The accurate dimensionality reduction model of the system is established, which facilitates the internal interpretation and physical control of the multistability that depends on the initial values. The dynamical behavior analyses of the dimensionality reduction memristive system with different original initial states are developed through bifurcation diagram and Lyapunov index spectrum. Multistability and antimonotonicity with periodic-chaotic bubbles are investigated. The sliding mode control method with a smooth function is designed to achieve the finite-time synchronization of the multistable memristive neuron systems, which make three different behaviors of systems synchronized. The sliding mode controller can enable the system to quickly and smoothly implement combination synchronization within finite time. Numerical simulations show the effectiveness of the sliding mode controller designed.
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