Bifurcations and Chaos in the Duffing Equation with Parametric Excitation and Single External Forcing

DOI10.1142/S0218127417501255zbMath1377.34047OpenAlexW2745041239MaRDI QIDQ4599784

Tao Jiang, Zhu-jun Jing, Zhi-Yan Yang

Publication date: 5 January 2018

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

Full work available at URL: https://doi.org/10.1142/s0218127417501255

zbMATH Keywords

bifurcationschaotic attractorsthe Duffing equationthe Melnikov methodthe second order averaging method

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Forced motions for nonlinear problems in mechanics (70K40) Perturbations of ordinary differential equations (34D10) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Averaging method for ordinary differential equations (34C29) Complex behavior and chaotic systems of ordinary differential equations (34C28) Parametric resonances for nonlinear problems in mechanics (70K28) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37)

Related Items (5)

On resonances under quasi-periodic perturbations of systems with a double limit cycle, close to two-dimensional nonlinear Hamiltonian systems ⋮ Link between externally excited nonlinear system and parametrically excited Duffing oscillator via bursting oscillations and phase transitions ⋮ The Coexisting Behaviors on the Boundary of a Duffing-like Oscillator with Signum Nonlinearity and Its FPGA-Based Implementation ⋮ Study on a Multi-Frequency Homotopy Analysis Method for Period-Doubling Solutions of Nonlinear Systems ⋮ Phenomena of Bifurcation and Chaos in the Dynamically Loaded Hyperelastic Spherical Membrane Based on a Noninteger Power-Law Constitutive Model

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