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Bifurcations of nontwisted heteroclinic loop with resonant eigenvalues
Yinlai Jin1, Xiaowei Zhu2, Zheng Guo1
1School of Science, Linyi University, Linyi, Shandong 276005, China.
Thescientificworldjournal
|June 4, 2014
Summary
This study analyzes bifurcation problems for nontwisted heteroclinic loops with resonant eigenvalues. It establishes the existence and regions for various loops and periodic orbits, providing bifurcation surfaces.
Area of Science:
- Dynamical Systems and Bifurcation Theory
- Mathematical Physics
Background:
- Heteroclinic orbits are crucial in understanding complex dynamical systems.
- Resonant eigenvalues introduce challenges in analyzing bifurcations.
Purpose of the Study:
- To investigate bifurcation problems of nontwisted heteroclinic loops with resonant eigenvalues.
- To determine the existence, number, and regions of various orbital structures.
Main Methods:
- Establishing local coordinate systems using foundational solutions of linear variational equations.
- Analyzing orbits in tubular neighborhoods of heteroclinic orbits.
Main Results:
- Existence, number, and regions for 1-heteroclinic loops, 1-homoclinic loops, and 1-periodic orbits.
- Identification of 2-fold 1-periodic orbits and pairs of 1-periodic orbits.
- Determination of corresponding bifurcation surfaces.
Conclusions:
- The study provides a comprehensive analysis of bifurcations in systems with resonant heteroclinic loops.
- The findings contribute to the understanding of complex dynamics and orbital structures.
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