Suppressing spiral waves in a lattice array of coupled neurons using delayed asymmetric synapse coupling

Abstract

Abstract The coupling between neuronal oscillator plays a significant role in their network performance. When the coupling is asymmetric in an electrical synapse connection, the entire dynamical behaviour of the neuron model changes. Such asymmetric synapse coupling on neuron models exposed to magnetic flux induction will display more complex behaviours. Hence, we propose a coupled neuron model considering flux coupling with asymmetric electrical synapse. The various dynamical properties of the coupled neuron model are explored by considering the coupling coefficients and flux coupling constant as the control parameters. The coexistence of at least chaotic with chaotic or chaotic with periodic or periodic with periodic firing patterns are identified in the new model for different values of coupling strengths. Such coexisting firing patters are also seen for discrete values of the flux coupling coefficient. The investigation is expanded further to the network performance of such coupled neurons considering the coupling coefficient as the parameter of discussion. A simple applied plane wave is disturbed and rotating spiral waves are formed in the network for different values of the coupling strength. We have shown that by introducing magnetic flux coupling into the neuron model, we could suppress the spiral waves in the network. As an alternative by considering a coupled neuron model without flux coupling and with delayed asymmetric electrical synapse coupling, we showed that the spiral waves are completely suppressed effectively for selected values of delay. Using delayed coupling comparatively more effective than flux coupling for supressing spiral waves in the network.