1 March 1994 Parametric entrainment of systems governed by ordinary differential equations
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Abstract
For systems represented by ordinary differential equations of a general form, it is shown that time dependencies for the parameters may be determined to generate new behaviors. These new dynamics are mathematical solutions determined using a second set of equations. Under many circumstances the system's new driven behavior entrains to these solutions in a stable manner. The method is explored via numerical simulation of a Duffing-like oscillator system. The results of these computer studies are then applied to an experimental system. A model consisting of a system of ordinary differential equations is determined for the experiment. The parametric driving term is computed and then applied. The response of the system is compared to the response from a sinusoidal driving force of similar characteristics and the results discussed.
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Russel D. Shermer, Russel D. Shermer, Mark L. Spano, Mark L. Spano, } "Parametric entrainment of systems governed by ordinary differential equations", Proc. SPIE 2037, Chaos/Nonlinear Dynamics: Methods and Commercialization, (1 March 1994); doi: 10.1117/12.167514; https://doi.org/10.1117/12.167514
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