Abstract
The transmission of information between neurons is accomplished in living organisms through synapses. The memristor is an electronic component that simulates the tunability of the strength of biological synaptic connections in artificial neural networks. This article constructs a novel type of locally active memristor and verifies by nonlinear theoretical analysis, locally active analysis and circuit simulation. The designed memristor is simulated as a biological autapse of Hindmarsh-Rose(HR) neuron to obtain the improved HR neuron model of memristive autapse, and the Hamilton energy is obtained according to Helmholtz theorem. By varying the external forcing current and the memristive autapse strength, this article analyses the changes of the Hamilton energy and explores its self-excited and hidden firing behavior. The analog circuit simulation and digital circuit implementation of the HR model confirm the consistency between the mathematical model and the actual behavior, which can advance the field of neuroscience and artificial intelligence.
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