Stabilizing topological states in a dynamic network of FitzHugh-Nagumo systems

We report how strategic evolution can stabilize topological states in a network of FitzHugh-Nagumo systems. The evolution follows a repeated process of adding or deleting of links between two nodes that is decided based on a threshold set for the closeness between them. This results in a need based rewiring that keeps the systems in synchrony in a single cluster or in phase locked states in different clusters. We analyse in detail the occurrence of such multi stable topological fixed points with corresponding emergent dynamical states using the frequency of occurrence of each state when evolved from a large number of initial states. We find that there is an optimum range for the threshold used in the strategy that results in maximum frequency for the stable topological states.