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A hyperchaotic time-delayed system with single-humped nonlinearity: theory and experiment

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Abstract

We propose a time-delayed hyperchaotic system with a single-humped nonlinearity that can be implemented in a controlled way using off-the-shelf electronic circuit elements. The proposed system is simple in design yet complex in its dynamical behavior. A rigorous stability analysis reveals that the system gives birth to a limit cycle via a supercritical Hopf bifurcation and also theoretical analysis predicts the occurrence of higher periodic cycles with increasing time delay. The complexity of the system is characterized by phase plane plots, bifurcation diagram and Lyapunov exponent spectrum. The system is implemented in an electronic circuit, and a data acquisition system is used to control the relevant circuit parameter to visualize the experimental bifurcation diagram. Experimental observations qualitatively support the analytical and numerical results. We believe that the present study will improve our understanding of the dynamical behavior of time-delayed systems with single-humped nonlinearity, which are very much relevant in physiological systems.

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Acknowledgements

D.B. acknowledges the financial support provided by the CSIR, India. T.B. acknowledges the financial support from SERB (DST) [SB/FTP/PS-005/2013].

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Authors and Affiliations

  1. Chaos and Complex Systems Research Laboratory, Department of Physics, University of Burdwan, Burdwan, West Bengal, 713 104, India

    Debabrata Biswas, Biswajit Karmakar & Tanmoy Banerjee

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  1. Debabrata Biswas
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  2. Biswajit Karmakar
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  3. Tanmoy Banerjee
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Correspondence to Tanmoy Banerjee.

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Biswas, D., Karmakar, B. & Banerjee, T. A hyperchaotic time-delayed system with single-humped nonlinearity: theory and experiment. Nonlinear Dyn 89, 1733–1743 (2017). https://doi.org/10.1007/s11071-017-3548-4

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  • DOI: https://doi.org/10.1007/s11071-017-3548-4

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