DETERMINISTIC CHAOS SEEN IN TERMS OF FEEDBACK CIRCUITS: ANALYSIS, SYNTHESIS, "LABYRINTH CHAOS"

Abstract

This paper aims to show how complex nonlinear dynamic systems can be classified, analyzed and synthesized in terms of feedback circuits. The Rössler equations for deterministic chaos are revisited and generalized in this perspective. It is shown that once a proper set of feedback circuits is present in the Jacobian matrix of the system, the chaotic character of trajectories is remarkably robust versus changes in the nature of the nonlinearities. "Labyrinth chaos", whereby simple differential systems generate large lattices of many unstable steady states embedded in a chaotic attractor, is constructed using this technique. In the limit case of a single three-element circuit without diagonal elements, one finds systems possessing an infinite lattice of unstable steady states between which trajectories percolate in a deterministic chaotic way.