Exact solutions for the quadratic mixed-parity Helmholtz-Duffing oscillator by bifurcation theory of dynamical systems

DOI10.1016/j.chaos.2015.08.021zbMath1355.34059OpenAlexW1602650215MaRDI QIDQ508487

Yixiang Geng

Publication date: 7 February 2017

Published in: Chaos, Solitons and Fractals (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.chaos.2015.08.021

zbMATH Keywords

periodic solutionbifurcation theorysoliton solutionkink solutionHelmholtz-Duffing oscillatoranti-kink solution

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Explicit solutions, first integrals of ordinary differential equations (34A05) Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations (34C10) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15)

Related Items (1)

The frequency estimation for non‐conservative nonlinear oscillation

Cites Work

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• Exact solution of the quadratic mixed-parity Helmholtz-Duffing oscillator
• Analytical solution of the damped Helmholtz-Duffing equation
• The iterative homotopy harmonic balance method for conservative Helmholtz-Duffing oscillators
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Traveling wave solutions for a class of nonlinear dispersive equations
• Exact travelling wave solutions for the \((n + 1)\)-dimensional double sine- and sinh-Gordon equations
• Exact explicit traveling wave solutions for the CDF equation
• Approximate periodic solutions for the Helmholtz-Duffing equation
• Symmetry-breaking analysis for the general Helmholtz-Duffing oscillator
• DYNAMIC BIFURCATIONS IN A POWER SYSTEM MODEL EXHIBITING VOLTAGE COLLAPSE
• Smooth and non-smooth traveling waves in a nonlinearly dispersive equation

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