Dynamics of Generalized Time Dependent Predator Prey Model with Nonlinear Harvesting (original) (raw)

In this paper, we consider the system of nonlinear ordinary differential equation ˙ x = x(t)(1 − x(t)) − a(t)f (x(t) ,y (t)) − h(t)γ(x(t)) ˙ y = y(t)(−d(t )+ b(t)g(x(t) ,y (t))) − k(t)ρ(y(t)) with t ≥ 0 and initial conditions x(0) = x0 > 0, y(0) = y0 > 0 and a, b, c, d, h, k and f, g are continuous from [0, ∞ )t o (0, ∞), ρ, γ are continuous from [0, ∞ )t o [0, ∞). Boundedness of solution(often called permanence) of this system is proved under suitable assumptions on the functions involved. Different examples of predator prey models are discussed as an application of the result. At last equilibria of some models are computed and their stability is analyzed.

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