Abstract
Two types of neuron models are constructed in this paper, namely the single discrete memristive synaptic neuron model and the dual discrete memristive synaptic neuron model. Firstly, it is proved that both models have only one unstable equilibrium point. Then, the influence of the coupling strength parameters and neural membrane amplification coefficient of the corresponding system of the two models on the rich dynamical behavior of the systems is analyzed. Research has shown that when the number of discrete local active memristor used as simulation synapses in the system increases from one to two, the coupling strength parameter of the same memristor has significantly different effects on the dynamical behavior of the system within the same range, that is, from a state with periodicity, chaos, and periodicity window to a state with only chaos. In addition, under the influence of coupling strength parameters and neural membrane amplification coefficients, the complexity of the system weakens to varying degrees. Moreover, under the effect of two memristors, the system exhibits a rare and interesting phenomenon where the coupling strength parameter and the neural membrane amplification coefficient can mutually serve as control parameter, resulting in the generation of a remerging Feigenbaum tree. Finally, the pseudo-randomness of the chaotic systems corresponding to the two models are detected by NIST SP800-22, and relevant simulation results are verified on the DSP hardware experimental platform. The discrete memristive synaptic neuron models established in this article provide assistance in studying the relevant working principles of real neurons.