Interplay of flux-controlled memristive synapse and Josephson junction properties in modified Morris-Lecar neuron dynamics.

In this work, we investigate the role of magnetic flux and Josephson junction (JJ) properties in the network of modified Morris Lecar (mML) neuron model. We begin our analysis by plotting bifurcation and Lyapunov spectrum for single coupled mML model. It exhibits both periodic and hyperchaotic dynamics for specific parameter ranges when considering both flux and the Josephson junction. Further, we plot the error plots to analyses the synchrony effect among neurons. Then we extend our analysis to a network of coupled mML neurons. Our study deals with three distinctive scenarios: Firstly, the regular network model where rewiring probability r is zero, the nodes are symmetrically connect to their 5 closest neighbors on either sides. Secondly, the small world network model, in which we introduced a modification by assigning $r=0.5$ , causing 50 percentages of connected nodes to be randomly reconnected. Lastly, the random network model, where we pushed the rewiring probability to its maximum, resulting in each node being arbitrarily linked to 10 nodes. Collective behaviour of all the three cases will be discussed and analyzed using spatiotemporal plots and recurrence plots. Our analysis shows that when the nodes are connected randomly, a lower value of coupling strength in both flux and JJ is sufficient to achieve synchronous behavior among the neurons or nodes. However, when the nodes are connected in a regular manner, higher coupling strengths are required to achieve coherent behavior among the neurons.