Chemically coupled Hindmarsh–Rose neurons with cross interactions between membrane potential and magnetic flux

Abstract

In this work, we have analysed the synchronous dynamics and pattern formation in Hindmarsh–Rose neurons with cross interactions between membrane potential and magnetic flux, in the chemical mode. The self, mixed and cross interactions are realised by varying coupling phase. The magnetic flux induces plateau bursting and amplitude death in the network. The self chemical coupling induces synchrony, whereas, the cross coupling is incapable of it. However, the cross coupling acts along with self coupling to form mixed coupling and induces synchrony in the system. The stability of the synchronous state has been studied by master stability approach. The parameter space reveals the bifurcation point at which cross coupling overrides self coupling effects. The synchronising ability of interactions are justified in a network of neurons as well. The statistical factor of synchronisation quantifies the amount of synchrony in the network in different interaction modes. The combined effect of non local interactions and mixed coupling of variables initiates the emergence of chimera and multichimera states. However, in cross-coupled systems, only incoherent states are present. The existence of chimera and multichimera states are confirmed by calculating the strength of incoherence and discontinuity measure. The analysis of spatiotemporal patterns reveals the presence of travelling chimeras within the network. The Hamilton energy function indicate that a greater amount of energy is required to sustain coherent neurons at higher potential. This work may enhance the understanding of chimera states and improve its applicability to real-world systems.