Order to chaos and vice versa in an aquatic ecosystem

Chaotic situation may arise from equilibrium state for different reasons in any ecosystem. But to overcome this chaotic situation sometimes system itself has some mechanism and self-adaptability. In aquatic system of such condition it is reported that toxins are produced by many phytoplankton and these toxins may turn the ecosystem in to ordered state from chaos by reducing the grazing pressure of zooplankton. In this paper a three species (phytoplankton, zooplankton and fish) model is proposed. The model is run in two different conditions. First, it has been considered that there is no toxin production from phytoplankton and in this condition the system exhibits different states (equilibrium point - stable limit cycle - doubling and ultimately chaos) by gradual decreasing of zooplankton body size. Decrement of zooplankton body size is controlled by increasing zooplankton grazing rate and decreasing the half saturation constant of zooplankton following allometric principles. When the system is in chaos, a toxin production parameter is introduced in the model equation. This toxin, produced from phytoplankton reduces the grazing pressure of zooplankton on phytoplankton. Gradually toxin values of phytoplankton are increased in the model which turn the system dynamics from chaos to doubling state to limit cycle and the system finally settles down to an equilibrium point.