Are three frequency quasiperiodic orbits to be expected in typical nonlinear dynamical systems?: 559 (M1,T3) Celso Grebogi, Laboratory for Plasma and Fusion Energy Studies, and Department of Physics and Astronomy; Edward Ott, Laboratory for Plasma and Fusion Energy Studies and Department of Electrical Engineering and Department of Physics and Astronomy; James A. Yorke, Department of Mathematics, and Institute for Physical

Abstract

We achieve control of deterministic chaos in an ecosystem model, involving three first-order nonlinear differential equations with a control parameter, recently proposed by Hastings and Powell (HP) in order to describe the dynamical behavior of a three-species food chain. After identifying a chaotic attractor corresponding to a particular value of the parameter of this ecological model, we locate periodic saddle orbits embedded in it. By applying the Ott–Grebogi–Yorke (OGY) method of controlling chaos, which introduces small time-dependent perturbations on the system parameter, we stabilize two of the saddle orbits. Furthermore, we check the versatility of the OGY method, as the system behavior is allowed to switch between ‘no control’ and ‘control’ about one or other of different stabilized periodic orbits.