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Control of noisy chaotic motion in a system with nonlinear excitation and restoring forces. (English) Zbl 0936.34035

Summary: The authors examine complex and chaotic oscillations of a dynamical system with nonlinear excitation and restoring forces for the purpose of controlling these oscillatory states. The physical system, modeled as a system of first-order nonlinear ordinary differential equations, takes into account a geometric nonlinearity in the restoring force, a quadratic viscous drag, and a harmonic excitation force. It is controlled using small perturbations about a selected unstable cycle and the control is instigated for periodic cycles of varying periodicities. The controller, when applied to the dynamical system with additive random noise in the excitation, successfully controls the system with noise levels in excess of 5% of the total energy, giving the first evidence that (stochastic) control of these systems is possible.

MSC:

34C28 Complex behavior and chaotic systems of ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C60 Qualitative investigation and simulation of ordinary differential equation models
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