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Complex dynamics and synchronization in two non-identical chaotic ecological systems

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  • Upadhyay, Ranjit Kumar
  • Rai, Vikas

Abstract

Synchronization is a natural phenomenon in non-linear dynamical systems. The relative importance of various mechanisms of population synchrony has been debated by population ecologists. The debate revolves around the issue whether the regionally extrinsic or locally intrinsic agents are more potent. In the present paper, we have attempted to demonstrate that a local intrinsic mechanism, predation, can be more common cause of population synchrony than is believed. Two chaotic food chains having different kinds of top-predators are synchronized using a recently proposed algorithm by Lu and Cao [Lu J, Cao J. Adaptive complete synchronization of two identical or different chaotic (hyperchaotic) dynamical systems with fully unknown parameters. Chaos 2005;15(043901):1–10]. The idiosyncracy of this approach is that it takes care of the uncertainties involved in the parameter estimation. The complete synchronization achieved is robust to noise present in the system. We suggest that local intrinsic causes of population synchrony should be given more attention.

Suggested Citation

  • Upadhyay, Ranjit Kumar & Rai, Vikas, 2009. "Complex dynamics and synchronization in two non-identical chaotic ecological systems," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2233-2241.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:5:p:2233-2241
    DOI: 10.1016/j.chaos.2007.10.016
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    References listed on IDEAS

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    1. Lei, Youming & Xu, Wei & Xie, Wenxian, 2007. "Synchronization of two chaotic four-dimensional systems using active control," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1823-1829.
    2. Chen, Hsien-Keng, 2005. "Global chaos synchronization of new chaotic systems via nonlinear control," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1245-1251.
    3. Rolf A. Ims & Harry P. Andreassen, 2000. "Spatial synchronization of vole population dynamics by predatory birds," Nature, Nature, vol. 408(6809), pages 194-196, November.
    4. Rai, Vikas & Upadhyay, Ranjit Kumar, 2006. "Evolving to the edge of chaos: Chance or necessity?," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1074-1087.
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    Cited by:

    1. Nikhil Pal & Sudip Samanta & Maia Martcheva & Joydev Chattopadhyay, 2018. "Role of Bi-Directional Migration in Two Similar Types of Ecosystems," Mathematics, MDPI, vol. 6(3), pages 1-16, March.
    2. Lee, S.H. & Park, M.J. & Kwon, O.M. & Sakthivel, R., 2016. "Master-slave synchronization for nonlinear systems via reliable control with gaussian stochastic process," Applied Mathematics and Computation, Elsevier, vol. 290(C), pages 439-459.

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