Indian Journal of Science and Technology

Abstract

Objectives: This study involves a three species fishery system having two prey and two predators (one species act as both prey and predator simultaneously). A discrete non-autonomous system of difference model for this three species preypredator model is proposed and analyzed. Methods/Statistical Analysis: The zooplankton (predator) grows based on the phytoplankton (prey) population. For the fish population the food sources are the phytoplankton (prey) population and zooplankton (prey) populations. The interesting part is that the toxin released by the Phytoplankton causes death to Zooplankton and controls the growth of Zooplankton population and also the death rate of Zooplankton is relative to the Phytoplankton population. The functional responses for Phytoplankton, Zooplankton and Fish population are of Holling type-II. Findings: A discrete non autonomous system of difference equations which governs P-Z-F model are analyzed under certain conditions on the parameters the existence of lowera and a upper boundsa of the a densities ofa all the three species are identified for established the permanence of the P-Z-F system and existence of a uniquea globallya stable periodica solutiona. It is also established under certaina conditions athe prey species will tend to global solution as the predator species become null. Application /Improvements: In this discrete non autonomous model, introducing density restriction terms for zooplankton and fish populations. The results indicate that, death rate of predator is very high or the conservative of Fish for Phytoplankton and Zooplankton are very small, then the Fish population will be driven to extinction.

Keywords: Fish, Global Stability, Periodic Solution, Permanence, Phytoplankton, Semi-Saturation Constant, Zooplankton