Hamiltonian energy and coexistence of spiral wave patterns in lattice array from bidirectional coupled neurons

Abstract In this study, we explore a Hindmarsh–Rose model to evaluate the impacts of asymmetric coupling, mutual interference, and external magnetic flux, as these factors play crucial roles in neurons dynamics. The performance of these networks is largely dependent on the coupling between neural oscillators. The entire neuron model’s dynamical behavior is altered when an electrical synapse connection has an asymmetric coupling. More complicated behaviors will be displayed by neuron models exposed to magnetic flux induction with such asymmetric synaptic coupling. As a result, we provide a coupled neuron model that takes into account asymmetric electrical synapses and flux coupling. The different dynamic features of the coupled Hindmarsh–Rose neuron model are investigated by taking the coupling, diffusion, and flux coupling coefficients constant into performance as the control factors. We have demonstrated that the integration of magnetic flux that enters the neuronal model can significantly attenuate spiral wave activity within the network. This approach mitigates the propagation of these waves and enhances the stability of the neural network. The supply and release of energy are significant for the functioning of individual neurons and neural networks. This paper investigates the Hamiltonian energy of neurons under electromagnetic induction, offering new insights into the interaction between neuronal dynamics and external electromagnetic fields.