A Novel Second-Order Memristor-Coupled FHN Neuron Model with Synergistic Dynamics of Multistability

With the rapid development of neuromorphic computing and brain-like intelligence technology, memristors show great potential in constructing artificial neural networks, but most of the existing memristors are still at the stage with simulating neuronal synapses, which cannot simulate the synaptic connections of neurons and electromagnetic radiation at the same time. Therefore, in this paper, a novel second-order memristor is designed. First, the nonvolatile nature of the memristor is verified, and second, a second-order memristor is introduced into neurons, where one order of the memristor is used as synapses and the other as electromagnetic radiation, and the dynamical behavior of the system is investigated by various analytical methods, such as bifurcation diagrams and Lyapunov exponents. To verify the engineering applicability of the theoretical results, this paper further successfully reproduces the key dynamical behaviors through circuit simulation and a DSP-based hardware experimental platform, realizing the systematic research flow from theoretical modeling, numerical simulation to circuit implementation and hardware verification. This not only confirms the physical realizability of the model, but also provides an experimental basis for the application of memristors in neuromorphic computing and brain-like intelligence.