FPGA-based Experimental Validations of Electrical Activities in Two Adjacent FitzHugh–Nagumo Neurons Coupled by Memristive Electromagnetic Induction

Abstract

ABSTRACT With the consideration of electromagnetic induction generated by the difference of membrane potentials between two adjacent neurons, a five-dimensional (5-D) memristor-coupled FitzHugh–Nagumo (FHN) bi-neuron model derived from connecting two FHN neurons with the memristive electromagnetic induction is presented. Then, with the 5-D memristor-coupled FHN bi-neuron model, the equilibrium states and their stabilities are explored by theoretical and numerical analyses. It is indicated that the proposed model has two non-zero equilibrium states with the same stability of unstable saddle-focus or unstable saddle point associating to the considered model parameters. The parameter-associated electrical activities of periodic, quasi-periodic, and chaotic behaviors are disclosed by bifurcation plots, dynamical maps, phase plane plots and further confirmed by 0–1 tests. Besides, the phenomena of initial-associated bi-stability with the coexistence of chaotic and periodic behaviors, as well as the riddled attraction basin, are revealed by local attraction basins and phase plane plots. Furthermore, based on field programmable gate array (FPGA), a digitally implemented electronic circuit is made, from which the electrical activities are experimentally captured to verify the numerical ones.