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Chaos to order: role of toxin producing phytoplankton in aquatic systems. (English) Zbl 1147.92327
Summary: Toxin producing phytoplankton (TPP) plays an important role in aquatic systems. To observe the role of TPP, we consider a three species food chain model consisting of TPP-zooplankton-fish populations. A similar type of models is considered by R. K. Upadhyay, S. R. K. Iyengar and V. Rai [Int. J. Bifurcation Chaos Appl. Sci. Eng. 8, No. 6, 1325–1333 (1998; Zbl 0935.92037)] for terrestrial ecosystems and they obtained chaotic dynamics in some region of the parameter space. We modify their models by taking into account the toxin liberation process of TPP populations represented as aquatic systems. We consider Holling type I, type II and type III functional forms for this process. We observe that increasing the strength of toxic substance changes the state from chaos to order. Our conclusion is that TPP has a stabilizing contribution in aquatic systems and may be used as a bio-control mechanism.

MSC:
92D40 Ecology
37N25 Dynamical systems in biology
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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