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Analysis of 4D autonomous system with volume-expanding phase space

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Abstract

This paper investigates the dynamics of four-dimensional autonomous oscillator with antiparallel diodes. A rare phenomenon of volume-expanding phase space is observed from the proposed model, and the only equilibrium point at the origin is found to be a repeller. Systems of this kind pave the way for the better understanding of repellers. In addition, the oscillator possesses extremely rich dynamical behaviors, including 2-tori, 3-tori (triple tori), limit cycles, chaos and hyperchaos. These dynamical behaviors are characterized with the help of the Lyapunov spectrum, bifurcation diagram, recurrence analysis, Poincaré surface of section, 0–1 test etc., Period doubling and torus breakdown to chaos are the predominant routes observed in the system for different parametric choices. The results of the real-time circuit are quite compatible with the numerical predictions.

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Acknowledgments

A.J would like to thank DST for the financial assistance in the form of DST INSPIRE Fellowship. P.P acknowledges University Grants Commission (UGC) for the financial support for this research work through a major research project F. No.41-961/2012(SR) dt. 0172012. S.S. acknowledges University Grants Commission (UGC) for the financial assistance through RFSMS scheme and K.T. acknowledges DST, Govt. of India.

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Authors and Affiliations

  1. PG and Research Department of Physics, A.V.V.M Sri Pushpam College, Poondi, Thanjavur, 613 503, India

    A. Jeevarekha & P. Philominathan

  2. Centre for Nonlinear Dynamics, School of Physics, Bharathidasan University, Tiruchirappalli, 620 024, India

    S. Sabarathinam & K. Thamilmaran

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  1. A. Jeevarekha
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  2. S. Sabarathinam
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  3. K. Thamilmaran
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  4. P. Philominathan
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Correspondence to P. Philominathan.

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Jeevarekha, A., Sabarathinam, S., Thamilmaran, K. et al. Analysis of 4D autonomous system with volume-expanding phase space. Nonlinear Dyn 84, 2273–2284 (2016). https://doi.org/10.1007/s11071-016-2644-1

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  • DOI: https://doi.org/10.1007/s11071-016-2644-1

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