Analysis of autonomous Lotka–Volterra competition systems with random perturbation

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.…”

Dynamical Analysis of a Class of Prey-Predator Model with Beddington-DeAngelis Functional Response, Stochastic Perturbation, and Impulsive Toxicant Input

“…Recently, various models based on stochastic differential equations (SDEs) have extensively been paid the attention of the researchers (see, e.g., [28][29][30][31][32][33][34][35][36][37]). Parameter perturbation induced by white noise is an important and common form to describe the effect of stochasticity (see, e.g., [37][38][39][40][41][42][43][44][45][46][47][48]). In this paper, we consider the white noise perturbation for the intrinsic growth rates of the prey and predator; that is, 1 → 1 + 11 ( ) and 2 → 2 + 22 ( ), where 1 ( ), 2 ( ) are mutually independent Brownian motions and 1 , 2 denote the intensities of the white noise.…”

On a non-autonomous stochastic Lotka-Volterra competitive system

“…Bao et al [7] investigated model (1.2) with Lévy jumps. Jiang et al [16] considered persistence and extinction of model (1.2) in autonomous case. However, model (1.2) is based on the assumption that only the growth rates r i are affected by the stochastic noise.…”