Ott-Grebogi-Yorke Research Articles

Controlling spatiotemporal chaos in a chain of the coupled logistic maps

A method of controlling spatiotemporal chaos in a chain of the logistic maps, based on the Ott, Grebogi, Yorke (OGY) approach, is proposed in the paper. Forms of spatiotemporal disturbances of a system parameter are determined analytically to stabilize desired spatiotemporal states. The results are illustrated by numerical experiments. Transitions of the system under control from the regime of spatiotemporal chaos to the regular homogeneous regime with temporal period one, two, four, and also to more complicated regular regimes with different spatial and temporal periods have been demonstrated. >

History-dependent control of unstable periodic orbits.

We present a method of stabilizing unstable periodic orbits in systems whose natural time scales are on the order of or faster than the time it would take for the experimental implementation of the Ott-Grebogi-Yorke (OGY) controlling method [Phys. Rev. Lett. 64, 1196 (1990)]. We determine the controlling perturbation one or more cycles ahead of when it needs to be applied, thereby gaining the additional time necessary to measure a signal, determine the perturbation, and then implement it. Formulas for this method of prior iterate control are derived and their utility is demonstrated numerically on the H\'enon map for controlling the unstable orbits of period one and two. The effects of noise on this control method are examined and the results are compared with a similar application of the OGY scheme in the presence of noise.

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

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.