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Evolving to the edge of chaos: Chance or necessity?

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  • Rai, Vikas
  • Upadhyay, Ranjit Kumar

Abstract

We show that ecological systems evolve to edges of chaos (EOC). This has been demonstrated by analyzing three diverse model ecosystems using numerical simulations in combination with analytical procedures. It has been found that all these systems reside on EOC and display short-term recurrent chaos (strc). The first two are non-linear food chains and the third one is a linear food chain. The dynamics of first two is dictated by deterministic changes in system parameters. In contrast to this, dynamics of the third model system (the linear food chain) is governed by both deterministic changes in system parameters as well as exogenous stochastic perturbations (unforeseen changes in initial conditions) of these dynamical systems.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:30:y:2006:i:5:p:1074-1087
    DOI: 10.1016/j.chaos.2005.09.003
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    1. Kevin McCann & Alan Hastings & Gary R. Huxel, 1998. "Weak trophic interactions and the balance of nature," Nature, Nature, vol. 395(6704), pages 794-798, October.
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    1. 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.
    2. Upadhyay, Ranjit Kumar & Kumari, Nitu & Rai, Vikas, 2009. "Exploring dynamical complexity in diffusion driven predator–prey systems: Effect of toxin producing phytoplankton and spatial heterogeneities," Chaos, Solitons & Fractals, Elsevier, vol. 42(1), pages 584-594.
    3. Upadhyay, Ranjit Kumar & Rao, V. Sree Hari, 2009. "Short-term recurrent chaos and role of Toxin Producing Phytoplankton (TPP) on chaotic dynamics in aquatic systems," Chaos, Solitons & Fractals, Elsevier, vol. 39(4), pages 1550-1564.

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