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Short-term recurrent chaos and role of Toxin Producing Phytoplankton (TPP) on chaotic dynamics in aquatic systems

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  • Upadhyay, Ranjit Kumar
  • Rao, V. Sree Hari

Abstract

We propose a new mathematical model for aquatic populations. This model incorporates mutual interference in all the three populations and an extra mortality term in zooplankton population and also taking into account the toxin liberation process of TPP population. The proposed model generalizes several other known models in the literature. The principal interest in this paper is in a numerical study of the model’s behaviour. It is observed that both types of food chains display same type of chaotic behaviour, short-term recurrent chaos, with different generating mechanisms. Toxin producing phytoplankton (TPP) reduces the grazing pressure of zooplankton. To observe the role of TPP, we consider Holling types I, II and III functional forms for this process. Our study suggests that toxic substances released by TPP population may act as bio-control by changing the state of chaos to order and extinction.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:chsofr:v:39:y:2009:i:4:p:1550-1564
    DOI: 10.1016/j.chaos.2007.06.132
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    1. 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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