73 research outputs found
Renormalization Group Method and its Application to Coupled Oscillators (Mathematical Aspects for nonlinear problems related to Life-phenomena)
Periodic orbits and chaos in fast-slow systems with Bogdanov-Takens type fold points
The existence of stable periodic orbits and chaotic invariant sets of
singularly perturbed problems of fast-slow type having Bogdanov-Takens
bifurcation points in its fast subsystem is proved by means of the geometric
singular perturbation method and the blow-up method. In particular, the blow-up
method is effectively used for analyzing the flow near the Bogdanov-Takens type
fold point in order to show that a slow manifold near the fold point is
extended along the Boutroux's tritronqu\'{e}e solution of the first
Painlev\'{e} equation in the blow-up space
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