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Effects of Random Excitations on the Dynamical Response of Duffing Systems

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Abstract

We study the dynamics of a Duffing oscillator excited by correlated random perturbations for both fixed and periodically modulated stiffness. In the case of fixed stiffness we see that Poincaré map gets distorted due to the random excitation and, the distortion increases with the increase of correlation of the field. In a strongly correlated field, however, the map becomes purely random. We analyse the maximum value of the Lyapunov exponent and see that the random response competes with the chaotic motion to increase the stability of the system. In the case of periodically modulated stiffness, the periodic parametric excitation causes the Duffing system to execute dynamics of two fixed-point attractors. These attractors remain non-chaotic even in the presence of random field but can get merged due to induced fluctuation in the trajectory. It is seen that the random field can change the status of the system from transit to stable state.

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Acknowledgements

G.S. would like to thank Professor Antun Balaz (Institute of Physics Belgrade, Serbia) for his suggestion on the generation of random potential. He would also like to thank Dr. Debaldev Jana (SRM University, India) for some useful discussion on the analysis of Lyapunov exponent.

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Authors and Affiliations

  1. Department of Physics, Banwarilal Bhalotia College, Asansol, 713303, India

    Kajal Krishna Dey

  2. Department of Physics, Kazi Nazrul University, Asansol, 713340, India

    Golam Ali Sekh

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  1. Kajal Krishna Dey
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  2. Golam Ali Sekh
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Correspondence to Golam Ali Sekh.

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Communicated by Chris Jarzynski.

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Dey, K.K., Sekh, G.A. Effects of Random Excitations on the Dynamical Response of Duffing Systems. J Stat Phys 182, 18 (2021). https://doi.org/10.1007/s10955-020-02694-x

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