Homoclinic twist bifurcations with \(\mathbb{Z}_ 2\) symmetry

DOI10.1007/BF02430632zbMath0799.58052MaRDI QIDQ1330861

D. G. Aronson, Martin Krupa, Stephan A. van Gils

Publication date: 10 August 1994

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

zbMATH Keywords

periodic orbitsbifurcationshomoclinic orbits\(\mathbb{Z}_ 2\) symmetry

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Local and nonlocal bifurcation theory for dynamical systems (37G99)

Related Items (6)

Robust heteroclinic cycles ⋮ Detecting symmetry breaking bifurcations in the system describing the dynamics of coupled arrays of Josephson junctions ⋮ Homoclinic flip bifurcation with a nonhyperbolic equilibrium ⋮ The cusp horseshoe and its bifurcations in the unfolding of an inclination-flip homoclinic orbit ⋮ Homoclinic flip bifurcations accompanied by transcritical bifurcation ⋮ About Convergence of Numerical Approximations to Homoclinic Twist Bifurcation Points in Z₂-Symmetric Systems in ℝ⁴

Uses Software

• AUTO

Cites Work

• Unnamed Item
• Homoclinic twisting bifurcations and cusp horseshoe maps
• Branching of double pulse solutions from single pulse solutions in nerve axon equations
• Singularities and groups in bifurcation theory. Volume II
• On the Structure of Local Homeomorphisms of Euclidean n-Space, II
• Coupled arrays of Josephson junctions and bifurcation of maps with S_Nsymmetry
• The cusp horseshoe and its bifurcations in the unfolding of an inclination-flip homoclinic orbit
• Global aspects of homoclinic bifurcations of vector fields

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