Bifurcation dynamics and FPGA implementation of coupled Fitzhugh-Nagumo neuronal system

This paper is devoted to studying the dynamical behaviors of the coupled FHN neural system by the discrete implicit mapping method, including bifurcation, coexistence, firing behaviors and synchronization. Two improved Fitzhugh-Nagumo (FHN) neurons are coupled through an asymmetric electrical synapse to investigate the effect of coupling strength on the firing behavior of neuronal networks, which is crucial to the progress of brain science. The types and stability of time-varying equilibrium points in the FHN neuron model are studied, and the corresponding discrete mapping model is established. The unstable periodic orbits hidden in chaos in the system are explored, and the mechanism of various bifurcations is explained through global eigenvalues. Simultaneously, the coexistence firing patterns are studied by basin of attraction, and the synchronization behavior of neural system is investigated through the normalized mean synchronization error (NMSE). Moreover, FPGA is employed for circuit implementation of the coupled neuronal system, and the correctness of theoretical results is verified. The results of this paper may help to better understand the firing and synchronization mechanisms of neural networks, which have important significance for the treatment of nervous system diseases and the development of neuroscience.