Coexistence bifurcation and FPGA implementation in memristive coupled Fitzhugh-Nagumo neural system

This paper focuses on the investigation of the memristive coupled FitzHugh-Nagumo (FHN) neural system through a discrete implicit mapping approach, which provides a significant support for the investigation of the coupling mechanism of complex neuronal networks. In this system, the original and improved FHN neurons are coupled via ideal memristors, the line equilibrium point of the system is examined, and a discrete mapping model describing the memristive coupled neural system is constructed. The system's unstable periodic orbits are predicted, and the stability along with the bifurcation types is analyzed from the viewpoint of global eigenvalues. The coexistence of reverse period-adding and period-doubling bifurcations is investigated, and the anti-monotonicity behavior depending on the coupling strength is studied. In addition, the extreme events under the influence of initial states are found in the system, the normalized mean synchronization error (NMSE) is given to study the synchronization and firing behavior. Finally, hardware circuit experiments based on field programmable gate array (FPGA) are carried out, which verify the correctness of the theoretical analysis. This paper offers a novel viewpoint for analyzing memristive coupled neural systems, which contributes to a deeper understanding of the complex dynamic behavior of neural networks and advance in brain science.