Homoclinic flip bifurcation with a nonhyperbolic equilibrium |
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| Authors: | Xingbo Liu Lina Shi Dongmei Zhang |
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| Institution: | 1. Department of Mathematics, East China Normal University, 200241, Shanghai, China
2. Department of Mathematics, Linyi University, 276005, Shandong, China
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| Abstract: | In this paper, the problem of homoclinic bifurcation accompanied by a transcritical bifurcation is investigated for high-dimensional systems. With the aid of a suitable local coordinate system, the Poincaré map is constructed. Under certain nongeneric conditions (orbit flip and inclination flip homoclinic orbits), the existence, nonexistence, coexistence and uniqueness of homoclinic and periodic orbits are studied. Some known results are extended. |
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