Resonant homoclinic flips bifurcation in principal eigendirections

DOI10.1155/2013/267826zbMath1343.37038OpenAlexW2018079878WikidataQ58915739 ScholiaQ58915739MaRDI QIDQ2015288

Xiaoxin Huang, De-Ming Zhu, Tian-Si Zhang

Publication date: 23 June 2014

Published in: Abstract and Applied Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1155/2013/267826

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Homoclinic and heteroclinic orbits for dynamical systems (37C29) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Cites Work

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• Global bifurcations and chaos. Analytical methods
• Bifurcations of heteroclinic loops
• Homoclinic flip bifurcations accompanied by transcritical bifurcation
• Bifurcations to \(N\)-homoclinic orbits and \(N\)-periodic orbits in vector fields
• Homoclinic bifurcation of orbit flip with resonant principal eigenvalues
• Inclination-flip homoclinic orbits arising from orbit-flip
• Numerical unfoldings of codimension-three resonant homoclinic flip bifurcations
• BIFURCATIONS OF HOMOCLINIC ORBIT CONNECTING TWO NONLEADING EIGENDIRECTIONS
• BIFURCATIONS OF GENERIC HETEROCLINIC LOOP ACCOMPANIED BY TRANSCRITICAL BIFURCATION
• HETERODIMENSIONAL CYCLE BIFURCATION WITH ORBIT-FLIP
• A strange attractor in the unfolding of an orbit-flip homoclinic orbit
• Strange attractor in the unfolding of an inclination-flip homoclinic orbit
• Resonant homoclinic flip bifurcations

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