A Study On Multi Ecological System Consisting Of Three Species A Prey, Predator And Neutralism

Abstract

Predation is the interaction where one species gets benefits at the expense of the other. In this interaction between two organisms one organism captures bio-mass from another. This is called as predator. In this interaction one organism eats away the another with its closeness of association. The lack of interaction between components of a mixed organism is known as neutralism. Despite coexisting, the species do not know one another, do not hurt one another, and do not benefit one another. In this paper, we study on multi ecological system consisting of three species (S₁, S₂, S₃) a prey, predator and neutralism with mortality rates. Here S₁ is the prey of two predators (S₂, S₃), the second and third species are neutrals. Three simultaneous non-linear first ordinary differential equations make up the mathematical model equations. There are recognized criteria for each of the eight equilibrium states' asymptotic stability. When all real roots are found to be negative and for complex roots having negative real part, the system become stable. Illustrations are provided for the perturbation trajectories over the equilibrium states. Additionally, the system's global stability is achieved by appropriately establishing Liapunov's function.