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Volume 20,     Number 2,     Summer 2012

 

ROLE OF CONSTANT NUTRIENT INPUT AND
MORTALITY RATE OF PLANKTIVOROUS FISH
IN PLANKTON COMMUNITY ECOSYSTEM
WITH INSTANTANEOUS NUTRIENT
RECYCLING
SAMARES PAL AND ANAL CHATTERJEE

Abstract. We consider the mathematical formulation, analysis, and numerical solution of a 'nutrient-phytoplankton- zooplankton-fish' model in an open marine system. We introduce higher predator fish in a Nutrient-Phytoplankton-Zoo- plankton model which depends on zooplankton. For a realistic representation of the open marine plankton ecosystem, we have incorporated various natural phenomena such as dissolved limiting nutrient with nutrient uptake function and instantaneous nutrient recycling. For the model with constant nutrient input and di erent constant washout rates, conditions for boundedness of the solutions, existence and stability of nonnegative equilibria are given. It is observed that constant nutrient input plays a vital role in changing the steady state behavior of the system. It further is observed that the mortality rate of the sh population plays an important role in changing steady state to oscillatory behavior of the system. Finally, it is observed that if the constant nutrient input crosses a certain critical value, the system enters into Hopf bifurcation. Computer simulations illustrate the results.

 

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