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Taming Non-autonomous Chaos in Duffing System Using Small Harmonic Perturbation

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Advances in Mathematical Modelling, Applied Analysis and Computation (ICMMAAC 2023)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 953))

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Abstract

In this work, three different classes of the excited models of Duffing system have been considered. In the considered Duffing models, for mathematical simplicity, only linear damping term is included. The various parameters values controlling the complex dynamics are so chosen that each of the models exhibit chaotic strange behavior in their corresponding phase-portraits, Poincare surface of sections and bifurcation diagram when excited sinusoidally with an amplitude, F and frequency \(\omega \). Unlike the usual method of feedback control, we explore the application of non-feedback control by directly adding a weak additional external periodic perturbation of frequency, \(\varOmega \), to control the chaos in these models. Incorporating such a perturbation term, bifurcation diagram have been reconstructed to ascertain critical values of the perturbation parameters transforming the chaotic response in the foregoing models to regular behavior. The non-feedback control, in the form of additional small harmonic perturbation term involving such critical parameters, has been shown to result in phase portraits showing the effectiveness of controlling the observed complex chaotic dynamics to regular dynamical response.

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Acknowledgment

Authors thank the referees, editors for their encouragement and constructive suggestions.

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Authors and Affiliations

  1. Department of Physics, Sri Venkateswara College, University of Delhi South Campus, Benito-JuarejRoad, New Delhi, 110021, India

    Anunay K. Chaudhary

  2. Institute of Informatics and Communication, University of Delhi South Campus, Benito -Juarej Road, New Delhi, 110021, India

    Saureesh Das & M. K. Das

  3. Department of Physics, A.R.S.D. College, University of Delhi South Campus, Dhaula Kuan, New Delhi, 110021, India

    Pankaj Narang

  4. Symbiosis Centre for Management Studies, Noida, India

    Anindita Bhattacharjee

  5. Symbiosis International (Deemed University), Pune, India

    Anindita Bhattacharjee

Authors
  1. Anunay K. Chaudhary
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  2. Saureesh Das
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  3. Pankaj Narang
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  4. Anindita Bhattacharjee
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  5. M. K. Das
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Corresponding author

Correspondence to M. K. Das .

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Editors and Affiliations

  1. Department of Mathematics, JECRC University, Jaipur, Rajasthan, India

    Jagdev Singh

  2. Department of Mathematics, University of Memphis, Memphis, TN, USA

    George A. Anastassiou

  3. Department of Computer Science and Mathematics, Lebanese American University, Beirut, Lebanon

    Dumitru Baleanu

  4. Department of Mathematics, University of Rajasthan, Jaipur, Rajasthan, India

    Devendra Kumar

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Chaudhary, A.K., Das, S., Narang, P., Bhattacharjee, A., Das, M.K. (2024). Taming Non-autonomous Chaos in Duffing System Using Small Harmonic Perturbation. In: Singh, J., Anastassiou, G.A., Baleanu, D., Kumar, D. (eds) Advances in Mathematical Modelling, Applied Analysis and Computation . ICMMAAC 2023. Lecture Notes in Networks and Systems, vol 953. Springer, Cham. https://doi.org/10.1007/978-3-031-56304-1_7

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  • DOI: https://doi.org/10.1007/978-3-031-56304-1_7

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  • Online ISBN: 978-3-031-56304-1

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