Heteroclinic cycles and modulated travelling waves in a system with \(D_ 4\) symmetry

DOI10.1016/0167-2789(92)90206-3zbMath0774.34031OpenAlexW1978470815MaRDI QIDQ1207216

Philip J. Holmes, Sue Ann Campbell

Publication date: 1 April 1993

Published in: Physica D (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-2789(92)90206-3

zbMATH Keywords

periodic orbitsbifurcationpersistencemethod of averagingquasiperiodic solutionsnumerical simulationssymmetry breakingMelnikov's methodregular modulated travelling wavessystem of two complex ordinary differential equations with \(D_ 4\) symmetry

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Bifurcation theory for ordinary differential equations (34C23) Almost and pseudo-almost periodic solutions to ordinary differential equations (34C27) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items

Transverse bifurcations of homoclinic cycles, Wavelet projections of the Kuramoto-Sivashinsky equation. I: Heteroclinic cycles and modulated traveling waves for short systems, Robust heteroclinic cycles, Suppression of bursting, Global bifurcations in the Takens-Bogdanov normal form with \(D_4\) symmetry near the \(O(2)\) limit, Dynamics in the 1:2 spatial resonance with broken reflection symmetry, Gröbner bases, invariant theory and equivariant dynamics, Pinning and locking of discrete waves

Uses Software

• Mathematica
• DSTool

Cites Work

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