Parametric entrainment of systems governed by ordinary differential equations

Russel D. Shermer; Mark L. Spano

doi:10.1117/12.167514

1 March 1994 Parametric entrainment of systems governed by ordinary differential equations

Russel D. Shermer, Mark L. Spano

Proceedings Volume 2037, Chaos/Nonlinear Dynamics: Methods and Commercialization; (1994) https://doi.org/10.1117/12.167514
Event: SPIE's 1993 International Symposium on Optics, Imaging, and Instrumentation, 1993, San Diego, CA, United States

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.

Citation Download Citation

Russel D. Shermer and Mark L. Spano "Parametric entrainment of systems governed by ordinary differential equations", Proc. SPIE 2037, Chaos/Nonlinear Dynamics: Methods and Commercialization, (1 March 1994); https://doi.org/10.1117/12.167514

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