Perturbation technique to analyze nonlinear oscillations
Using perturbation and asymptotic methods, the author analyzes the nonlinear oscillations of two dynamical systems: the Bonhoeffer-van der Pol equations and the forced Duffing equation. In the two-dimensional model of the former system, he studies the transition from stable steady-state to relaxation oscillation as a parameter is varied. The analysis also helps to clarify a phenomenon commonly known as the duck trajectory. In the three-dimensional model, bursting oscillation is explained. In the forced Duffing equation, the main interest is the trajectory near the homoclinic orbit and the saddle point. A map of that trajectory is analytically constructed. From that map, limit cycles and their linear stability are investigated.
- Research Organization:
- Northwestern Univ., Evanston, IL (USA)
- OSTI ID:
- 6681353
- Resource Relation:
- Other Information: Thesis (Ph. D.)
- Country of Publication:
- United States
- Language:
- English
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