A theory of orbital behavior in a class of nonlinear systems: Chaos and a signature-based approach

摘要

A theory of orbital behavior in certain autonomous one-dimensional nonlinear systems is pursued, using an approach based upon the concept of (orbital) signature. Particular attention is paid to the fixed point structure of such systems with the ultimate aim of using the signature repertoires of these systems to characterize fixed-point orders and the presence of chaos. A system-theoretic approach is pursued here: an approach which complements other recent studies of a more analytical nature. Chaotic behavior in a certain subclass of these system is completely characterized in terms of the first two iterates of a specific known point in the range of the system transition function.