scholarly journals Dynamical Analysis Predator-Prey Population with Holling Type II Functional Response

2021 ◽  
Author(s):  
FE. Universitas Andi Djemma

In this article, we investigate the dynamical analysis of predator prey model. Interactionamong preys and predators use Holling type II functional response, and assuming prey refuge aswell as harvesting in both populations. This study aims to study the predator prey model and todetermine the effect of overharvesting which consequently will affect the ecosystem. In the modelfound three equilibrium points, i.e., (0,0) is the extinction of predator and prey equilibrium,?(??, 0) is the equilibrium with predatory populations extinct and the last equilibrium points?(??, ??) is the coexist equilibrium. All equilibrium points are asymptotically stable (locally) undercertain conditions. These analytical findings were confirmed by several numerical simulations.

2020 ◽  
Vol 2020 ◽  
pp. 1-17
Author(s):  
C. Gokila ◽  
M. Sambath ◽  
K. Balachandran ◽  
Yong-Ki Ma

A stochastic predator-prey model with disease in the prey and Holling type II functional response is proposed and its dynamics is analyzed. We discuss the boundedness of the dynamical system and find all feasible equilibrium solutions. For the stochastic systems, we obtain the conditions for the existence of the global unique solution, boundedness, and uniform continuity. We derive the conditions for extinction and permanence of species. Moreover, we construct appropriate Lyapunov functions and discuss the asymptotic stability of equilibria. To illustrate our theoretical findings, we have performed numerical simulations and presented the results.


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