Codimension 2 bifurcations of double homoclinic loops

DOI10.1016/j.chaos.2007.01.101zbMath1197.37065OpenAlexW2030372868MaRDI QIDQ711882

Weipeng Zhang, De-Ming Zhu

Publication date: 28 October 2010

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2007.01.101

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)

Related Items (4)

The twisting bifurcations of double homoclinic loops with resonant eigenvalues ⋮ Non-resonance 3D homoclinic bifurcation with an inclination flip ⋮ Multiple Buckling and Codimension-Three Bifurcation Phenomena of a Nonlinear Oscillator ⋮ NONRESONANT BIFURCATIONS OF HETEROCLINIC LOOPS WITH ONE INCLINATION FLIP

Cites Work

• Bifurcations of rough heteroclinic loop with two saddle points
• Homoclinic bifurcation at resonant eigenvalues
• Global bifurcations and chaos. Analytical methods
• Bifurcations of heteroclinic loops
• Constructing dynamical systems having homoclinic bifurcation points of codimension two
• Homoclinic bifurcations in heterogeneous market models.
• Prediction of homoclinic bifurcation: the elliptic averaging method
• Bifurcations of nontwisted heteroclinic loop.
• On the number of limit cycles in double homoclinic bifurcations
• Bifurcation of limit cycles and separatrix loops in singular Liénard systems
• Homoclinic bifurcation and chaos in simple pendulum under bounded noise excitation
• Homoclinic solutions for autonomous ordinary differential equations with nonautonomous perturbations
• Bifurcations for heteroclinic orbits of a periodic motion and a saddle-focus and dynamical chaos
• Global aspects of homoclinic bifurcations of three-dimensional saddles
• Bifurcations to \(N\)-homoclinic orbits and \(N\)-periodic orbits in vector fields
• Codimension 3 nonresonant bifurcations of homoclinic orbits with two inclination flips
• Numerical unfoldings of codimension-three resonant homoclinic flip bifurcations
• Homoclinic Solutions for Autonomous Dynamical Systems in Arbitrary Dimension
• MULTIPLE HOMOCLINIC BIFURCATIONS FROM ORBIT-FLIP I: SUCCESSIVE HOMOCLINIC DOUBLINGS
• CODIMENSION 3 HOMOCLINIC BIFURCATION OF ORBIT FLIP WITH RESONANT EIGENVALUES CORRESPONDING TO THE TANGENT DIRECTIONS
• Resonant homoclinic flip bifurcations

This page was built for publication: Codimension 2 bifurcations of double homoclinic loops