A coevolution model for dynamical networks of discrete-time chaotic systems

Dynamical networks are ensembles of dynamical systems connected with a given structure, which in most cases is assumed to be fixed. However, a more realistic situation is that in which the network topology has its own dynamics. To model a dynamical network with evolving topology is a challenging problem that has recently attracted considerable attention. In this contribution we propose to model the structural evolution of a dynamical network taking into consideration the interplay between the dynamics of the nodes and the processes that determine the structural changes of the network, that is, our model is focus on the coevolution of the dynamical network. In this work we consider a dynamical network with N identical nodes, where each one is a discrete-time chaotic system, namely, the Logistic map. We propose a set of iterative rules that determine the state of each link as either “on” (1) or “off” (0). The state of the link depends on both the states of the nodes which it connects and the structural features of the network. We observed that under node-centric coevolution rules, the network can be made to favor the emergence of a stable synchronized behavior as the structure changes towards a highly connected homogeneous topology. On the other hand, for link-centric coevolution rules, the network can be made to evolve towards a sparsely connected heterogeneous topology, however, the synchronization between its nodes is lost.