Computing Domains of Attraction for Planar Dynamics

In this note we investigate the problem of computing the domain of attraction of a flow on R2 for a given attractor. We consider an operator that takes two inputs, the description of the flow and a cover of the attractors, and outputs the domain of attraction for the given attractor. We show that: (i) if we consider only (structurally) stable systems, the operator is (strictly semi-)computable; (ii) if we allow all systems defined by C1 -functions, the operator is not (semi-)computable. We also address the problem of computing limit cycles on these systems. Many problems about dynamical systems (DSs) are concerned with their long term behavior. For example, given some trajectory, where will it end up? Which are the invariant sets of a DS? Which are its attractors? Recently, with the advent of increasingly powerful digital computers, numerous new ideas and concepts related to these question have appeared (e.g. sensitive dependence on initial conditions, chaos, strange attractors, Man...

• Type: Conference
• Year: 2009
• Where: UC
• Authors: Daniel S. Graça, Ning Zhong
• Keywords: Applied Computing, Initial Conditions, Lorenz Strange Attractor, Strange Attractor, UC 2009