ROBUST BURSTING TO THE ORIGIN: HETEROCLINIC CYCLES WITH MAXIMAL SYMMETRY EQUILIBRIA

DOI10.1142/S0218127405013708zbMath1093.37509WikidataQ61951262 ScholiaQ61951262MaRDI QIDQ5474326

David Hawker, Peter Ashwin

Publication date: 23 June 2006

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

robustsymmetrystabilitybifurcationheteroclinic cycles

Mathematics Subject Classification ID

Dynamical aspects of symmetries, equivariant bifurcation theory (37G40) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Homoclinic and heteroclinic orbits for dynamical systems (37C29)

Related Items (2)

Modelling instability \(ABC\) flow using a mode interaction between steady and Hopf bifurcations with rotational symmetries of the cube ⋮ Essentially asymptotically stable homoclinic networks

Cites Work

• Homoclinic bifurcation at resonant eigenvalues
• Heteroclinic cycles and modulated travelling waves in systems with 0(2) symmetry
• Transverse bifurcations of homoclinic cycles
• Robust heteroclinic cycles
• Heteroclinic networks in coupled cell systems
• Bursts in oscillatory systems with broken \(D_4\) symmetry
• Back in the Saddle Again: A Computer Assisted Study of the Kuramoto–Sivashinsky Equation
• Structurally stable heteroclinic cycles
• An example of a nonasymptotically stable attractor
• Stationary bifurcation to limit cycles and heteroclinic cycles
• A competition between heteroclinic cycles
• Heteroclinic cycles involving periodic solutions in mode interactions with O(2) symmetry
• Forced symmetry breaking of homoclinic cycles
• New type of complex dynamics in the \(1:2\) spatial resonance
• Unnamed Item

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