Double Hopf Bifurcation with Huygens Symmetry

DOI10.1137/110839461zbMath1284.34051OpenAlexW2163931868MaRDI QIDQ2871321

Petko M. Kitanov, Allan R. Willms, William F. Langford

Publication date: 22 January 2014

Published in: SIAM Journal on Applied Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/67a169d8513f1302508f420800e4c4f591c1fe1f

zbMATH Keywords

symmetrydouble Hopf bifurcationnonlinear resonanceequivariant bifurcation theorycoupled identical oscillatorsHuygens clockstoroidal breather

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Bifurcation theory for ordinary differential equations (34C23) Dynamical aspects of symmetries, equivariant bifurcation theory (37G40) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Invariant manifolds for ordinary differential equations (34C45) Nonlinear resonances for nonlinear problems in mechanics (70K30) Synchronization of solutions to ordinary differential equations (34D06) Multifrequency systems of ordinary differential equations (34C46)

Related Items (4)

Synchronization, symmetry and rotating periodic solutions in oscillators with Huygens' coupling ⋮ High-Order Approximation of Heteroclinic Bifurcations in Truncated 2D-Normal Forms for the Generic Cases of Hopf-Zero and Nonresonant Double Hopf Singularities ⋮ Slow–Fast Behaviors and Their Mechanism in a Periodically Excited Dynamical System with Double Hopf Bifurcations ⋮ A Degenerate 2:3 Resonant Hopf--Hopf Bifurcation as Organizing Center of the Dynamics: Numerical Semiglobal Results

Uses Software

• Matlab

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