Multiple Buckling and Codimension-Three Bifurcation Phenomena of a Nonlinear Oscillator

DOI10.1142/S0218127414300055zbMath1284.34050OpenAlexW2081524346MaRDI QIDQ5407284

Marian Wiercigroch, Ting-Wei Liang, Yanwei Han, Qing-jie Cao, Serguei Piskarev

Publication date: 7 April 2014

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

Full work available at URL: https://doi.org/10.1142/s0218127414300055

zbMATH Keywords

Melnikov's methodsingular closed orbitsmultiple bucklingrig-coupled SD oscillatortwo-parameter codimension-three bifurcation

Mathematics Subject Classification ID

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)

Stable Running with Asymmetric Legs: A Bifurcation Approach ⋮ Chaotic threshold for a class of impulsive differential system ⋮ An oscillator with two discontinuous lines and Van der Pol damping ⋮ Global dynamics for a class of tristable system with negative stiffness ⋮ Global studies on a continuous planar piecewise linear differential system with three zones ⋮ A Quintic \(\boldsymbol{\mathbb{Z}_2}\)-Equivariant Liénard System Arising from the Complex Ginzburg–Landau Equation ⋮ Contact Impact Forces at Discontinuous 2-DOF Vibroimpact ⋮ Subharmonic Melnikov theory for degenerate resonance systems and its application ⋮ Nonlinear Dynamics of a Smooth and Discontinuous Oscillator with Multiple Stability ⋮ Free vibration analysis of a structural system with a pair of irrational nonlinearities ⋮ Chaos Threshold of a Multistable Piezoelectric Energy Harvester Subjected to Wake-Galloping

Cites Work

• Unnamed Item
• Codimension-2 bifurcations of the Kaldor model of business cycle
• Nonlinear response of a forced van der Pol-Duffing oscillator at non-resonant bifurcations of codimension two
• Codimension 2 bifurcations of double homoclinic loops
• Codimension-two bifurcation analysis on firing activities in Chay neuron model
• Elliptic integrals and their nonoscillation
• Co-dimension two bifurcation analysis for two-dimensional plasma convection
• A system with three limit cycles appearing in a Hopf bifurcation and dying in a homoclinic bifurcation: The cusp of order 4
• Canard cycles of finite codimension with two breaking parameters
• On a codimension-three bifurcation arising in a simple dynamo model
• Equivariant multiparameter bifurcation via singularity theory
• The codimension-two bifurcation for the recent proposed SD oscillator
• Singular analysis of bifurcation systems with two parameters
• ESTIMATION OF CHAOTIC THRESHOLDS FOR THE RECENTLY PROPOSED ROTATING PENDULUM
• Codimension 2 Symmetric Homoclinic Bifurcations and Application to 1:2 Resonance
• Piecewise linear approach to an archetypal oscillator for smooth and discontinuous dynamics

This page was built for publication: Multiple Buckling and Codimension-Three Bifurcation Phenomena of a Nonlinear Oscillator