The Mutual Stabilization of Chaotic Systems and its Entropy

Recent work demonstrates how pairs of interacting classically-chaotic systems can be induced into persistent, periodic behavior, known as mutual stabilization, when information is exchanged between the two systems via an interaction function. In such a state, the chaotic behavior of each system is stabilized onto one of the system’s many unstable periodic orbits, and the ensuing periodicity of each system is then sustained via the symbolic dynamics of its partner system, and vice versa. Notably, mutual stabilization is an entropy-reversing event: the entropy of each member of a mutually-stabilized pair decreases to zero during each system’s collapse to the given period orbit. In this talk, we discuss the role that entropy plays in mutual stabilization. We also discuss the geometry that arises when pairs of mutually-stabilized chaotic systems organize into coherent structures that range in complexity from simple tripartite lattices to more involved patterns. The talk will conclude with a discussion of future research directions.