Abstract
In this paper, bidirectional-coupled neurons through an asymmetric electrical synapse are investigated. These coupled neurons involve 2D Hindmarsh–Rose (HR) and 2D FitzHugh–Nagumo (FN) neurons. The equilibria of the coupled neurons model are investigated, and their stabilities have revealed that, for some values of the electrical synaptic weight, the model under consideration can display either self-excited or hidden firing patterns. In addition, the hidden coexistence of chaotic bursting with periodic spiking, chaotic spiking with period spiking, chaotic bursting with a resting pattern, and the coexistence of chaotic spiking with a resting pattern are also found for some sets of electrical synaptic coupling. For all the investigated phenomena, the Hamiltonian energy of the model is computed. It enables the estimation of the amount of energy released during the transition between the various electrical activities. Pspice simulations are carried out based on the analog circuit of the coupled neurons to support our numerical results. Finally, an STM32F407ZE microcontroller development board is exploited for the digital implementation of the proposed coupled neurons model.
Highlights
The human brain is an organ that can exhibit extremely complex nonlinear behavior (Natarajan et al 2004)
The hidden coexistence of chaotic bursting with periodic spiking, chaotic spiking with period spiking, chaotic bursting with a resting pattern, and the coexistence of chaotic spiking with a resting pattern are found for some sets of electrical synaptic coupling
It is good to mention that such types of nonlinear behaviors involving multistability, hidden dynamics previously found in neurons were able to occur in circuits and systems, such as the extended Lu system(Lai et al 2018a), a unified chaotic system (Lai 2021), a two-memristor-based chaotic system (Lai et al 2020a) as well as a non-equilibrium chaotic system (Lai et al 2020b)
Summary
The human brain is an organ that can exhibit extremely complex nonlinear behavior (Natarajan et al 2004). Kafraj et al (Kafraj et al 2020) have introduced and investigated a three-variable memristive Izhikevich model to describe the behavior of neurons under electromagnetic induction and noise Their model represented the effect of internal and external magnetic fields on neurons. Njitacke et al (Tabekoueng Njitacke et al 2020) have considered the dynamics of two coupled 2D HR neurons with a small discrepancy of their parameters From their investigations, the authors found that their proposed simple 4D neural oscillator was able to exhibit traditional brain firing activities including bursting, spiking oscillations as well as the phenomenon of bistability under the variation of the symmetric coupling weight and the external stimulus. In the present contribution, we have investigated the complex dynamics of a simple heterogeneous neural network made of the coupling between a 2D HR neuron model with a 2D FN neuron model through asymmetric electrical synapses. Energy will be sufficient to maintain continuous electrical activities in the considered coupled neurons
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