Bursts in oscillatory systems with broken \(D_4\) symmetry

DOI10.1016/S0167-2789(99)00141-4zbMath0941.34024OpenAlexW2154408122MaRDI QIDQ1964025

Jeff Moehlis, Edgar Knoblauch

Publication date: 28 July 2000

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

Full work available at URL: https://doi.org/10.1016/s0167-2789(99)00141-4

zbMATH Keywords

burstsglobal bifurcationsheteroclinic cyclesforced symmetry-breakingHopf bifurcation with broken \(D_4\) symmetry

Mathematics Subject Classification ID

Symmetries, invariants of ordinary differential equations (34C14) Bifurcation theory for ordinary differential equations (34C23) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (11)

Heteroclinic dynamics in a model of Faraday waves in a square container ⋮ Arnold tongues in a billiard problem in nonlinear and nonequilibrium systems ⋮ Nonlinear dynamic behavior of a microbeam array subject to parametric actuation at low, medium and large DC-voltages ⋮ Oscillatory Marangoni convection in binary mixtures in square and nearly square containers ⋮ Global bifurcations in the Takens-Bogdanov normal form with \(D_4\) symmetry near the \(O(2)\) limit ⋮ Effect of noise on excursions to and back from infinity ⋮ Wrinkled tori and bursts due to resonant temporal forcing ⋮ Weakly coupled parametrically forced oscillator networks: existence, stability, and symmetry of solutions ⋮ Dynamics in the 1:2 spatial resonance with broken reflection symmetry ⋮ ROBUST BURSTING TO THE ORIGIN: HETEROCLINIC CYCLES WITH MAXIMAL SYMMETRY EQUILIBRIA ⋮ Homoclinic orbits near heteroclinic cycles with one equilibrium and one periodic orbit

Uses Software

• AUTO
• DSTool

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