Theory and Application of a Nongeneric Heteroclinic Loop Bifurcation
Copyright policy )Theory and Application of a Nongeneric Heteroclinic Loop Bifurcation
Summary: Homoclinic and heteroclinic bifurcations from a heteroclinic loop are considered. The system under consideration has three parameters, two of which are not suitable for generic unfoldings. Analytical criteria in terms of derivatives to Melnikov's functions are given for nongeneric parameters. Four qualitatively distinct bifurcation diagrams are obtained. The result is used to give an explanation of a numerical finding on the generation of traveling pulsing waves in a two-phase flow problem.
- Georgia Institute of Technology United States
- University of Alabama in Huntsville United States
Bifurcation theory for ordinary differential equations, Complex behavior and chaotic systems of ordinary differential equations, implicit function theorem, heteroclinic loop bifurcations, Nonlinear ordinary differential equations and systems, principal eigenvalues, Melnikov functions, Solitary waves for incompressible inviscid fluids, twisted and nontwisted heteroclinic orbits
Bifurcation theory for ordinary differential equations, Complex behavior and chaotic systems of ordinary differential equations, implicit function theorem, heteroclinic loop bifurcations, Nonlinear ordinary differential equations and systems, principal eigenvalues, Melnikov functions, Solitary waves for incompressible inviscid fluids, twisted and nontwisted heteroclinic orbits
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