Stochastic prey–predator model with additional food for predator

Extinction and ergodic stationary distribution of a Markovian-switching prey-predator model with additional food for predator

“…Initial values are taken at (2,3). By making use of the conditions of Theorem 5.4 in [24], we obtain that the prey population and the predator population coexist for a long time (See Fig. 1).…”

“…, so π = (0.4, 0.6). In system (1.2), we choose appropriate parameters: (r(1), r(2)) = (2, 1.5); (c 1 (1), c 1 (2)) = (1.4, 1.6), (a 1 (1), a 1 (2)) = (1, 1.5), (b 1 (1), b 1 (2)) = (1, 1.3), (α(1), α(2)) = (0.5, 0.4), (l(1), l(2)) = (0.4, 0.5) (ξ(1), ξ(2)) = (0.02, 0.025), K = 4 [24]. 1.…”

“…At the outset of our numerical simulation, we deal with the case only with white noise . Hence system (1.2) is reduced to the model in [24]. Let r = 2; c 1 = 1.2, a 1 = 1, b 1 = 1.3, α = 0.5, l = 0.4, ξ = 0.025, K = 4. σ 11 = 0.006, σ 12 = 0.001, σ 21 = 0.005, σ 22 = 0.001.…”

“…Recently predator-prey models in random environment have also gained much attention [17,19,20,21,22,23]. Das and Samanta [24] established a stochastic prey-predator model with additional food for predator. They studied the persistence of the system under obtained conditions and how the solution of the underlying system is globally attractive in mean.…”

“…Λ t is a continuous time Markov chain with a finite state space M = {1, 2, ..., n}, 1 ≤ n < ∞. Obviously, assuming no Markov chain Λ t , if σ i2 = 0 (i = 1, 2), our model becomes the system in [24]; if σ ij = 0 (i, j = 1, 2), our model becomes the system (1.1) with Holling type-II response. It should be noted that the present model is made more realistic by considering noises and predator-prey interference.…”