Heterogeneity induced control of chaotic systems to stable limit cycles

Abstract

We explore the behavior of coupled chaotic oscillators where one unit has intrinsically dissimilar dynamics. We find that the presence of a single dissimilar chaotic system in the network manages to drive all the chaotic oscillators to regular limit cycles. Additionally the regular cycles that emerge are significantly smaller in size than the uncoupled chaotic attractors. Counterintuitively the more geometrically dissimilar the single distinct system is from the other chaotic oscillators, the stronger is the emergent control. Furthermore, the position of the dissimilar system in the network does not affect the control when the dissimilar element is markedly different. So surprisingly, enhanced heterogeneity in coupled systems leads to more pronounced and robust controllability. Our results can then potentially lead to the design of new control strategies in engineered systems, and also suggests mechanisms whereby naturally occurring complex systems can evolve to regular dynamics through coupling to heterogeneous sub-systems.