Hidden electrical activity of two neurons connected with an asymmetric electric coupling subject to electromagnetic induction: Coexistence of patterns and its analog implementation - Njitacke, Zeric Tabekoueng; Doubla, Isaac Sami; Mabekou, Sandrine; Kengne, Jacques (Chaos, solitons and fractals, 2020)
•Model of electrical activity in a model of coupled 2D Hindmarsh-Rose neuron model under an asymmetric electrical coupling.•Effect of a threshold electromagnetic induction and emergences of hidden dynamics.•The space magnetization, characterized by the coexistence of different hidden stable states•Electronic implementation of the coupled neuron model using Pspice simulations In this paper, the effects of a threshold electromagnetic induction, as well as an asymmetry in the electrical synaptic coupling between two neuronal oscillators, are studied through a 2D Hindmarsh-Rose model. We have found that the introduced model has no-equilibrium point and thus, displays hidden dynamics. We equally demonstrate that the electromagnetic induction strength combined with an asymmetric electrical coupling and external stimulus induces the coexistence of bifurcations and multiple firing patterns in the coupled neural oscillators. The coexistence of at least two firing patterns including chaotic and periodic ones for some discrete values of the electromagnetic induction strength, coupling strengths, and external stimulus is demonstrated using time series, phase portraits, bifurcation diagrams, graph of maximum Lyapunov exponent, and basins of attraction. The PSpice results with analog electronic circuits are in good agreement with the results of theoretical analyses. To the best of the author's knowledge, the results of this work represent the first report on the phenomenon of coexistence of multiple firing patterns in a coupled 2D Hindmarsh-Rose model under threshold electromagnetic induction effect thus, deserve dissemination.