Constructing Continuous-Time Chaos-Generating Templates with Desirably Configured Periodic Orbits

Abstract

Towards extending the methodology for developing flexible pattern generators and controllers that can exploit various nonlinear phenomena, this paper proposes a framework for constructing continuous-time dynamical systems that bind desired unstable periodic orbits into a chaotic attractor. Our strategy is comprised of the following three stages: constructing an interim "chaos-generating template", deforming the template according to the desired configuration of periodic orbits, and performing appropriate function approximation to obtain the dynamical system.