A codimension-two resonant bifurcation from a heteroclinic cycle with complex eigenvalues

DOI10.1080/14689360600552928zbMath1132.34033OpenAlexW2142792878MaRDI QIDQ3426263

Jonathan H. P. Dawes, Claire M. Postlethwaite

Publication date: 8 March 2007

Published in: Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/14689360600552928

zbMATH Keywords

symmetrybifurcationperiodic orbitrobust heteroclinic cycle

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Symmetries, invariants of ordinary differential equations (34C14) Bifurcation theory for ordinary differential equations (34C23) Dynamical aspects of symmetries, equivariant bifurcation theory (37G40) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (11)

Stability of cycling behaviour near a heteroclinic network model of Rock–Paper–Scissors–Lizard–Spock ⋮ Bifurcations from an attracting heteroclinic cycle under periodic forcing ⋮ The effect of symmetry breaking on the dynamics near a structurally stable heteroclinic cycle between equilibria and a periodic orbit ⋮ Effect of noise on residence times of a heteroclinic cycle ⋮ Dynamics near a periodically-perturbed robust heteroclinic cycle ⋮ A trio of heteroclinic bifurcations arising from a model of spatially-extended Rock–Paper–Scissors ⋮ A low-dimensional model of binocular rivalry using winnerless competition ⋮ A new mechanism for stability loss from a heteroclinic cycle ⋮ A mechanism for switching near a heteroclinic network ⋮ Resonance bifurcation from homoclinic cycles ⋮ Noise-induced switching near a depth two heteroclinic network and an application to Boussinesq convection

Uses Software

• AUTO

Cites Work

• Homoclinic bifurcation at resonant eigenvalues
• Transverse bifurcations of homoclinic cycles
• Robust heteroclinic cycles
• Structurally stable heteroclinic cycles
• Stationary bifurcation to limit cycles and heteroclinic cycles
• Nonlinear Aspects of Competition Between Three Species
• Asymptotic stability of heteroclinic cycles in systems with symmetry
• Evolutionary Games and Population Dynamics
• Asymptotic stability of heteroclinic cycles in systems with symmetry. II
• Resonant homoclinic flip bifurcations

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