An FHN-HR Neuron Network Coupled With a Novel Locally Active Memristor and Its DSP Implementation

In this article, a novel locally active memristor (LAM) model is designed and its characteristics are studied in detail. Then, the LAM model is applied to couple FitzHugh-Nagumo (FHN) and Hindmarsh-Rose (HR) neuron. The simple neuron network is built to emulate connection of separate neurons and transmission of information from FHN neuron to HR neuron. The equilibrium point about this FHN-HR model is analyzed. Under the influence of varied parameters, dynamical characteristics for the model are explored with various analysis methods, including phase diagram, time series, bifurcation diagram, and Lyapunov exponent spectrum (LEs). The spectral entropy (SE) complexity and sequence randomness of the model are studied. In addition to observing chaotic and periodic attractors, multiple types of attractor coexistence and particular state transition phenomena are also found in the coupled FHN-HR model. Furthermore, geometric control is used for modulating the amplitude and offset of attractor and neuron firing signals, involving amplitude control and offset control. Finally, DSP implementation is finished, proving digital circuit feasibility of the FHN-HR model. The research imitates the coupling and information transmission between different neurons and has potential applications to secrecy or encryption.