Synchronisation Scenario and Emergence of Spatial Chimeras in 2D Lattice

This work analyses the emergence of spatial chimeras due to the interplay of electromagnetic, nonlinear, distance dependent and cross coupling in a network of Hindmarsh-Rose neurons. The neurons are arranged to form a square lattice. The electromagnetic induction produced by the flow of ions is represented using the memrsitor. The chemical coupling is inherently nonlinear. The distance between the neurons in the terms of lattice parameter ensures that the contribution decreases with increase in distance. The cross coupling is a non conventional method of coupling which enables the network to exhibit different interesting behaviours. The statistical factor of synchronisation is calculated to quantify the amount of synchrony in the network for different coordination numbers of the coupling neurons. The spatiotemporal analysis reveals that the spatial chimeras possess travelling nature. The Hamiltonian energy of the system derived using the Helmholtz theorem suggests that significant energy is utilised to maintain the membrane potential at high values regardless of polarity, while energy consumption is lower when the membrane potential approaches zero.