On Global Dynamics in Duffing Equation with Quasiperiodic Perturbation

DOI10.15507/2079-6900.22.202002.164-176OpenAlexW3038045708MaRDI QIDQ6143794

Kirill Morozov, Unnamed Author, Albert D. Morozov

Publication date: 24 January 2024

Published in: Zhurnal Srednevolzhskogo Matematicheskogo Obshchestva (Search for Journal in Brave)

Full work available at URL: http://mathnet.ru/eng/svmo766

zbMATH Keywords

homoclinic solutionsresonancesDuffing equationaveragingglobal dynamicsMelnikov methodtwo-dimensional dynamical systemsquasiperiodic perturbationMelnikov's formula

Mathematics Subject Classification ID

Forced motions for nonlinear problems in mechanics (70K40) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Averaging method for ordinary differential equations (34C29) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30) Perturbations, asymptotics of solutions to ordinary differential equations (34E10) Homoclinic and heteroclinic solutions to ordinary differential equations (34C37) Nonlinear resonances for nonlinear problems in mechanics (70K30)

Related Items (1)

On resonances under quasi-periodic perturbations of systems with a double limit cycle, close to two-dimensional nonlinear Hamiltonian systems

Cites Work

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• Second-order averaging and chaos in quasiperiodically forced weakly nonlinear oscillators
• Global bifurcations and chaos. Analytical methods
• Chaotic transport in dynamical systems
• Quasiperiodic resonance and bifurcations of tori in the weakly nonlinear Duffing oscillator
• Quasiperiodic perturbations of two-dimensional Hamiltonian systems
• Complex dynamics in Duffing system with two external forcings
• Complex dynamics in three-well Duffing system with two external forcings
• Melnikov's method and averaging

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