Driven damped nth-power anharmonic oscillators with time-dependent coefficients and their integrals of motion

Chaotic dynamics and subharmonic bifurcations of a soft Duffing oscillator with a non-smooth periodic perturbation and a harmonic excitation are investigated analytically in this paper. With the Fourier series, the system is expanded to the equivalent smooth system, and chaos arising from heteroclinic intersections is studied with the Melnikov method. The chaotic feature on the system parameters is investigated in detail. Some new interesting dynamic phenomena, such as chaotic bands for some excitation frequencies, are presented. The relationship between the frequency range of chaotic bands and the amplitude of the excitation as well as the damping is obtained analytically. Particularly, for some system parameters satisfying a particular relationship, chaos cannot occur for any excitation amplitudes or frequencies. Subharmonic bifurcations are investigated with a subharmonic Melnikov method. It is analytically proved that the system may undergo chaotic motions through infinite or finite odd order subharmonic bifurcations. Numerical simulations are given to verify the chaos threshold and revolution from subharmonic bifurcations to chaos obtained by analytical methods.

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An integral of motion for a Master–Slave system of damped Duffing oscillators with variable coefficients: Nonlinear dynamics and computer simulations

Barba-Franco,

Gallegos,

Urenda-Cázares

et al. 2024

Int. J. Mod. Phys. C

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In this work, a master–slave system composed by a pair of damped Duffing oscillators with variable coefficients and nonlinear coupling is investigated. An integral of motion for the system is obtained using a symmetry transformation and Noether’s theorem. Some numerical examples are presented for different cases of damping and oscillation frequency, for a varying coupling constant. The system dynamics is studied by means of space-time surfaces, time series and phase portraits. For a constant oscillation frequency, the slave presents envelopes that tend to become chaotic as the coupling constant increases. Meanwhile, as the frequency increases with time, the slave has higher amplitudes and speeds than the master oscillator.

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Driven damped nth-power anharmonic oscillators with time-dependent coefficients and their integrals of motion

Cited by 3 publications

References 24 publications

Integral of motion and nonlinear dynamics of three Duffing oscillators with weak or strong bidirectional coupling

Integral of motion and nonlinear dynamics of three Duffing oscillators with weak or strong bidirectional coupling

Chaos and subharmonic bifurcations of a soft Duffing oscillator with a non-smooth periodic perturbation and harmonic excitation

An integral of motion for a Master–Slave system of damped Duffing oscillators with variable coefficients: Nonlinear dynamics and computer simulations

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