ANALYTICAL APPROXIMATION OF HETEROCLINIC BIFURCATION IN A 1:4 RESONANCE

DOI10.1142/S021812741250294XzbMath1258.34090MaRDI QIDQ4908403

Abdelhak Fahsi, Mohamed Belhaq

Publication date: 5 March 2013

Published in: International Journal of Bifurcation and Chaos (Search for Journal in Brave)

zbMATH Keywords

frequency-lockingheteroclinic connection1:4 resonancecollision criteriondouble perturbation technique

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (7)

Periodic and quasiperiodic galloping of a wind-excited tower under external excitation ⋮ 1:2 and 1:4 resonances in a two-dimensional discrete Hindmarsh-Rose model ⋮ High-order study of the canard explosion in an aircraft ground dynamics model ⋮ Analysis of 1:4 resonance in a monopoly model with memory ⋮ Homoclinic-doubling and homoclinic-gluing bifurcations in the Takens-Bogdanov normal form with D4 symmetry ⋮ On the Heteroclinic Connections in the 1:3 Resonance Problem ⋮ Approximations of the Heteroclinic Orbits Near a Double-Zero Bifurcation with Symmetry of Order Two. Application to a Liénard Equation

Cites Work

• Analytics of heteroclinic bifurcation in a \(3:1\) subharmonic resonance
• 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
• Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields
• 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 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
• Quadratic non-linear oscillators
• ANALYTICS OF HOMOCLINIC BIFURCATIONS IN THREE-DIMENSIONAL SYSTEMS

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