Wiggins, Stephen and Holmes, Philip (1985) Slowly varying oscillators. In: 1985 24th IEEE Conference on Decision and Control. IEEE , Piscataway, NJ, p. 2051. https://resolver.caltech.edu/CaltechAUTHORS:20170725-172032835
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Abstract
We develop a Melnikov type perturbation method for detecting periodic and homoclinic orbits and codimension one bifurcations in a class of third order nonlinear ordinary differential equations. These equations may be autonomous or contain time periodic terms, but we assume that they are small perturbations of integrable Hamiltonian systems with unperturbed energy functions of the form H(x,y;z) and that the z-coordinate varies slowly in the perturbed system. We apply these methods to a nonlinear oscillator subject to weak feedback control.
| Item Type: | Book Section | |||||||||
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| Additional Information: | © 1985 IEEE. Research supported in part by the Air Force Office of Scientific Research under AFOSR 84-0051. | |||||||||
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| Record Number: | CaltechAUTHORS:20170725-172032835 | |||||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20170725-172032835 | |||||||||
| Official Citation: | S. Wiggins and P. Holmes, "Slowly varying oscillators," 1985 24th IEEE Conference on Decision and Control, Fort Lauderdale, FL, USA, 1985, pp. 2051-2051. doi: 10.1109/CDC.1985.268563 | |||||||||
| Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | |||||||||
| ID Code: | 79365 | |||||||||
| Collection: | CaltechAUTHORS | |||||||||
| Deposited By: | Kristin Buxton | |||||||||
| Deposited On: | 26 Jul 2017 22:50 | |||||||||
| Last Modified: | 03 Oct 2019 18:19 |
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