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Quadrature Synchronization of Two Van der Pol Oscillators Coupled by Fractional-Order Derivatives

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Progress in Advanced Computing and Intelligent Engineering

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 714))

Abstract

The paper presents a theoretical analysis of the synchronization behavior of two coupled Van der Pol oscillators, where the coupling is defined by fractional-order derivatives. The condition for frequency synchronization is obtained for the two oscillators being in-phase quadrature. It is found that the synchronization frequency oscillates rapidly with respect to the deviations from phase quadrature and the order of fractional derivative. The linear stability analysis is carried out by analyzing the roots of Jacobian on phase error.

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Acknowledgments

The author AKS is thankful to University Grants Commission (UGC, Govt. of India, Delhi) for financial assistance.

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Authors and Affiliations

  1. Sensors & Signal Processing Laboratory, Department of Physics, Institute of Science, Banaras Hindu University, Varanasi, 221005, India

    Aman K. Singh & R. D. S. Yadava

Authors
  1. Aman K. Singh
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  2. R. D. S. Yadava
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Corresponding author

Correspondence to Aman K. Singh .

Editor information

Editors and Affiliations

  1. Department of Computer Science, Rama Devi Women’s University, Bhubaneswar, Odisha, India

    Chhabi Rani Panigrahi

  2. Department of Computer Science, Central University of Rajasthan, Ajmer, Rajasthan, India

    Arun K. Pujari

  3. Department of Computer Science and Engineering, Indian Institute of Technology Kharagpur, Kharagpur, India

    Sudip Misra

  4. Department of Computer Science, Rama Devi Women’s University, Bhubaneswar, Odisha, India

    Bibudhendu Pati

  5. Department of Computer Science and Information Engineering (CSIE), Providence University, Taichung, Taiwan

    Kuan-Ching Li

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Singh, A.K., Yadava, R.D.S. (2019). Quadrature Synchronization of Two Van der Pol Oscillators Coupled by Fractional-Order Derivatives. In: Panigrahi, C., Pujari, A., Misra, S., Pati, B., Li, KC. (eds) Progress in Advanced Computing and Intelligent Engineering. Advances in Intelligent Systems and Computing, vol 714. Springer, Singapore. https://doi.org/10.1007/978-981-13-0224-4_53

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  • DOI: https://doi.org/10.1007/978-981-13-0224-4_53

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-0223-7

  • Online ISBN: 978-981-13-0224-4

  • eBook Packages: EngineeringEngineering (R0)

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