Bifurcations and stability of nondegenerated homoclinic loops for higher dimensional systems

DOI10.1155/2013/582820zbMath1307.34063OpenAlexW1999123830WikidataQ37351648 ScholiaQ37351648MaRDI QIDQ2262242

Feng Li, Jing Li, Han Xu, Benyan Ding, Li-Qun Zhang, Yin Lai Jin

Publication date: 16 March 2015

Published in: Computational \& Mathematical Methods in Medicine (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2013/582820

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Ecology (92D40) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (2)

Bifurcations of Heteroclinic Loop with Twisted Conditions ⋮ The contrast structures for a class of singularly perturbed systems with heteroclinic orbits

Cites Work

• Bifurcations of rough heteroclinic loop with two saddle points
• Exponential dichotomies, heteroclinic orbits, and Melnikov functions
• Homoclinic bifurcation at resonant eigenvalues
• The Sil'nikov problem, exponential expansion, strong \(\lambda\)-lemma, \(C^ 1\)-linearization, and homoclinic bifurcation
• Degenerated homoclinic bifurcations with higher dimensions
• Exponential dichotomies and transversal homoclinic points
• Twisted bifurcations and stability of homoclinic loop with higher dimensions
• Melnikov vector in higher dimensions
• Problems in homoclinic bifurcation with higher dimensions
• Stability and uniqueness of periodic orbits produced during homoclinic bifurcation

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