Mechanisms for the development of unstable dimension variability and the breakdown of shadowing in coupled chaotic systems.

Abstract

A chaotic attractor containing unstable periodic orbits with different numbers of unstable directions is said to exhibit unstable dimension variability (UDV). We present general mechanisms for the progressive development of UDV in uni- and bidirectionally coupled systems of chaotic elements. Our results are applicable to systems of dissimilar elements without invariant manifolds. We also quantify the severity of UDV to identify coupling ranges where the shadowability and modelability of such systems are significantly compromised.