Population dynamical behaviors of stochastic logistic system with jumps

Abstract

This paper is concerned with a stochastic logistic model driven by martingales with jumps. In the model, generalized noise and jump noise are taken into account. This model is new and more feasible. The explicit global positive solution of the system is presented, and then sufficient conditions for extinction and persistence are established.The critical value of extinction, nonpersistence in the mean, and weak persistence in the mean are obtained. The pathwise and moment properties are also investigated. Finally, some simulation figures are introduced to illustrate the main results.

Dynamical behaviors of stochastic eco‐epidemic predator–prey model with Allee effect in prey and Lévy jump

“…According to Lemma 2.5 in [25], let h = 1, 2, • • • , 𝜂 > 0, 𝜃 > 1, and 0 < 𝜀 < 1, then we can deduce that…”

Dynamics of a stochastic population model with Allee effect and jumps

“…Then, we continue to examine the stochastically ultimate boundedness of the model. Lemma 3.1 (see [16,24]). Let f : [0, ∞) → R and h : [0, ∞) × Γ → R be both predictable {F t }-adapted processes such that for any T > 0,…”

“…(ii) if r + β > 0, then lim t→∞ x(t) = r+β c a.s. Wu and Wang [24] discussed non-autonomous model corresponding to model (4.7). From [24], we know that the jump noise and the general noise can make the population extinct.…”

“…(ii) if r + β > 0, then lim t→∞ x(t) = r+β c a.s. Wu and Wang [24] discussed non-autonomous model corresponding to model (4.7). From [24], we know that the jump noise and the general noise can make the population extinct. [31] discussed the dynamics of a stochastic predator-prey model with habitat complexity and prey aggregation.…”