Chaos Due to Resonances in Physical Systems
Here we survey several applications of the theory developed in Chapter 2. The problems are picked from rigid body dynamics, fluid mechanics, atmospheric science, and nonlinear optics. Almost all physical models we study are dissipative and have been noted to display complex dynamics, yet the usual Melnikov method (see Section 1.27) does not reveal any chaotic behavior when applied to perturbations of their integrable limits. Rather, most of these models tend to develop their chaotic attractors, as the perturbation increases, around orbits homoclinic to slow or partially slow manifolds. While the techniques are still missing for the analytic study of such attractors, the attracting nature of heteroclinic cycles near resonances can be shown explicitly in some examples (cf. Section 3.7).
KeywordsUnstable Manifold Chaotic Attractor Homoclinic Orbit Modal Equation Heteroclinic Orbit
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