Stochastic persistence and stability analysis of a modified Holling–Tanner model

Abstract

The article aims to study the basic dynamical features of a modified Holling–Tanner prey–predator model with ratio‐dependent functional response. We have proved the global existence of the solution for the deterministic model. The parametric restriction for persistence of both species is also obtained along with the proof of local asymptotic stability of the interior equilibrium point(s). Conditions for local bifurcations of interior equilibrium points are provided. The global dynamic behavior is examined thoroughly with supportive numerical simulation results. Next, we have formulated the stochastic model by perturbing the intrinsic growth rates of prey and predator populations with white noise terms. The existence uniqueness of solutions for stochastic model is established. Further, we have derived the parametric restrictions required for the persistence of the stochastic model. Finally, we have discussed the stochastic stability results in terms of the first and second order moments. Numerical simulation results are provided to support the analytical findings. Copyright © 2012 John Wiley & Sons, Ltd.

Dynamic Analysis of a Modified Stochastic Predator-Prey System With General Ratio-Dependent Functional Response

“…We have established the persistent and extinct results for system (3). For a special case n = 1, system (3) is similar to that considered by Mandal and Banerjee [15]. The persistence of system (3) obtained in Theorem 4.4 are the same as Theorem 3.2 in [15].…”

“…Motivated by the works in [11,15,17,18], in this paper, we will study a modified stochastic predator-prey model with general ratio-dependent functional response as follows:…”

“…Then, based on system (2), Mandal and Banerjee [15] considered a modified stochastic predator-prey model with ratio-dependent functional response.…”

Analysis of a stochastic cooperation-competition model

“…These random factors of the environment are not only an integral part of any realistic ecosystem, but they also may lead to complete extinction of populations. The existing research works have investigated dynamic properties of stochastic predator-prey models [7][8][9][10][11][12], stochastic competitive models [13][14][15][16][17][18], stochastic mutualism models [19][20][21][22][23][24] and stochastic three-species models [25][26][27][28][29][30][31][32][33]. To the best of our knowledge, there are few studies to analyze the dynamics of a stochastic cooperation-competition model.…”

Dynamics of a Stochastic Intraguild Predation Model

“…In essence, random factors can lead to complete extinction of populations even if the population size is relatively large. Previous studies have explored the dynamic properties for stochastic single species models [14][15][16], stochastic predator-prey models [17][18][19][20][21][22][23], stochastic competitive models [24][25][26][27], stochastic mutualism model [28][29][30][31]. Specially, Liu and Wang [32] investigated a two-prey one-predator model with random perturbations.…”