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The Bifurcation of Homoclinic Cycles Accompanied with Transcritical Bifurcation

Author: ShiLiNa
Tutor: LiuXingBo
School: East China Normal University
Course: Applied Mathematics
Keywords: Supercritical branch Inclination flip Orbit flip Homoclinic orbit Heteroclinic orbit Periodic orbit
CLC: O175
Type: Master's thesis
Year: 2011
Downloads: 7
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Abstract


Differential equations bifurcation theory is an important part of the theory of differential equations , in many fields of science have an important role , especially in the chaos and the reaction of the traveling wave solutions of the diffusion equation , has been occupying an important position . Since local activities coordinate frame method appears, the branch issues a more extensive research . article focuses on two types accompanied by supercritical branch high - dimensional non-degenerate system in non -pass assumption homoclinic orbit branch Chapter II study is accompanied by supercritical branch high dimensional systems in simultaneous orbit flip and under inclination flip homoclinic orbit branch problem by building local activities coordinate frame , the establishment of the Poincare map , thereby After a simple calculation export system branch equation , the problem of transformation for the demand branch equation of non- negative solutions exist sex first discussed when the supercritical branch does not occur , homoclinic orbits , periodic orbits exist conditions ; Second assumptions accompanying supercritical branch get homoclinic orbits to save and sub- spending cycle track of conditions , which also consider the of inclination flips strength for the branch results . discussed in Chapter III homoclinic orbit branch problem in the case of two-track flip occurs accompanied by a high -dimensional system of supercritical branch , in some other non- generic assumptions , the same local activities coordinate frame to build the successor function , and then get a new branch equations . still from two aspects whether accompanied by supercritical branch after to discuss the existence of homoclinic orbits , save and sub ??expenditure cycle track conditions . At the same time , also get some of the results .

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CLC: > Mathematical sciences and chemical > Mathematics > Mathematical Analysis > Differential equations, integral equations
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