Symmetry breaking Hopf bifurcations in equation with O(2) symmetry with application to the Kuramoto-Sivashinsky equation

DOI10.1006/jcph.1996.5599zbMath0868.65038OpenAlexW2032771769MaRDI QIDQ676338

Faridon Amdjadi, Philip J. Aston, Petr Plecháč

Publication date: 18 August 1997

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jcph.1996.5599

zbMATH Keywords

eigenvalueKuramoto-Sivashinsky equationJacobian matrix\(O(2)\) symmetrymultiple Hopf bifurcations

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Numerical methods for initial value problems involving ordinary differential equations (65L05)

Related Items (4)

Low-dimensional dynamo modelling and symmetry-breaking bifurcations ⋮ Oscillating waves arising from \(\text{O}(2)\) symmetry. ⋮ Spatial period-multiplying instabilities of hexagonal Faraday waves ⋮ BIFURCATION FROM AN EQUILIBRIUM OF THE STEADY STATE KURAMOTO–SIVASHINSKY EQUATION IN TWO SPATIAL DIMENSIONS

Cites Work

• Chemical oscillations, waves, and turbulence
• Order and complexity in the Kuramoto-Sivashinsky model of weakly turbulent interfaces
• Computational methods for bifurcation problems with symmetries - with special attention to steady state and Hopf bifurcation points
• Singularities and groups in bifurcation theory. Volume II
• Phase Dynamics of Weakly Unstable Periodic Structures
• Analysis and Computation of Symmetry-Breaking Bifurcation and Scaling Laws Using Group-Theoretic Methods
• The Computation of Symmetry-Breaking Bifurcation Points
• Bifurcations of Relative Equilibria
• Nonlinear analysis of hydrodynamic instability in laminar flames—I. Derivation of basic equations
• Bifurcation to Rotating Waves in Equations with $O(2)$-Symmetry
• Numerical Methods for Steady State/Hopf Mode Interactions
• On a Reduction Process for Nonlinear Equations
• Local Numerical Analysis of Hopf Bifurcation
• Symmetry-based algorithms to relate partial differential equations: I. Local symmetries
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