Analytics of heteroclinic bifurcation in a \(3:1\) subharmonic resonance

DOI10.1007/s11071-010-9780-9zbMath1215.37037OpenAlexW1964612993MaRDI QIDQ547193

Abdelhak Fahsi, Mohamed Belhaq

Publication date: 30 June 2011

Published in: Nonlinear Dynamics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11071-010-9780-9

zbMATH Keywords

perturbation analysisfrequency-lockingheteroclinic bifurcation3:1 subharmonic resonancedouble reduction technique

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Bifurcations of singular points in dynamical systems (37G10)

Related Items (3)

Periodic and quasiperiodic galloping of a wind-excited tower under external excitation ⋮ ANALYTICAL APPROXIMATION OF HETEROCLINIC BIFURCATION IN A 1:4 RESONANCE ⋮ Homoclinic-doubling and homoclinic-gluing bifurcations in the Takens-Bogdanov normal form with D4 symmetry

Cites Work

• Hysteresis suppression and synchronization near 3:1 subharmonic resonance
• Asymptotic solutions for a damped non-linear quasi-periodic Mathieu equation
• Hysteresis suppression for primary and subharmonic 3:1 resonances using fast excitation
• 4-subharmonic bifurcation and homoclinic transition near resonance point in nonlinear parametric oscillator
• Quasi-periodic oscillations, chaos and suppression of chaos in a nonlinear oscillator driven by parametric and external excitations
• Predicting homoclinic bifurcations in planar autonomous systems
• Homoclinic bifurcations in self-excited oscillators
• 2:2:1 resonance in the quasiperiodic Mathieu equation
• Asymptotics of homoclinic bifurcation in a three-dimensional system
• Homoclinic connections in strongly self-excited nonlinear oscillators: The Melnikov function and the elliptic Lindstedt-Poincaré method
• Bifurcation to heteroclinic cycles and sensitivity in three and four coupled phase oscillators
• Three-period quasi-periodic solutions in the self-excited quasi-periodic Mathieu oscillator
• ANALYTICS OF HOMOCLINIC BIFURCATIONS IN THREE-DIMENSIONAL SYSTEMS
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