Dynamical networks: interplay of topology, interactions and local dynamics

摘要

Dynamical networks are characterized by their topology (structure of a network), by interactions between the elements (local subsystems) sitting at the nodes of a network and by intrinsic dynamics (local evolution) of these local subsystems. We analyse a joint action (interplay) of these three factors by the methods of symbolic dynamics and thermodynamic formalism. The main result provides sufficient conditions for stable evolution of dynamical networks and their subnetworks. No restrictions on the topology of a network are considered. Therefore, our results are applicable to dynamical networks with an arbitrary (random, regular, scale-free, small-world, etc) structure.