Bifurcations to bursting and spiking in the Chay neuron and their validation in a digital circuit

Abstract

Abstract Due to the great importance of the outward current carried by K+ions and the inward one by Na+ and Ca2+ions in 3-D Chay neuron model, the dynamical behaviors associated with the maximal conductances of K+ions channel and mixed Na+-Ca2+ions channel are explored for better demonstrating dynamical effects on the electrical activities in this paper. By utilizing some common dynamical exploring methods, the representative electrical activities of bursting and spiking behaviors endowed with the fast-slow structure of the 3-D Chay neuron model are revealed and classified on the dependence of the two maximal conductances. Moreover, the bifurcation mechanisms for periodic fold/fold bursting, periodic and chaotic fold/homoclinic bursting, and chaotic spiking behaviors are expounded qualitatively by fast-slow dynamical analysis with some specified model parameters. Finally, based on a field programmable gate array (FPGA), a digitally circuit-implemented electronic neuron is made, from which the chaotic and periodic bursting/spiking behaviors are experimentally captured to confirm the numerical simulations.