Optimal placement of a dissimilar node for chaos suppression in networks

Abstract

We demonstrate that the presence of a single dissimilar chaotic system suppresses chaos in networks of chaotic oscillators, in a diverse set of network topologies, for sufficiently strong coupling. The key property is determined to be the sum of the path lengths between the dissimilar node and all the other nodes (or its maximum, if coupled to unconnected networks), and there exists a linear relation between this quantity and the critical coupling strength for the onset of a spatiotemporal fixed point. This holds true for a chain with the dissimilar node at different locations, a ring and complete network with one embedded dissimilar node, as well as star networks with a dissimilar hub or dissimilar peripheral node. Furthermore, we show that networks with high average degree and high clustering coefficient are more resilient to the influence of an external dissimilar system. These findings will potentially aid in the design of optimally placed dissimilar nodes for controlling chaos in complex networks.