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This work is concerned with a two-species stochastic state-switching competitive population model with distributed delays and harvesting. First, necessary and sufficient criteria for the existence of a unique ergodic stationary distribution of the system are established. Then necessary and sufficient criteria for the existence of the optimal harvesting policy are given, and the explicit expression of the optimal harvesting policy is obtained. Finally, some effects of the state-switching on the persistence, extinction and optimal harvesting strategy of the system are discussed with the help of several simulations. [ABSTRACT FROM AUTHOR]

This paper systematically investigates the optimal harvesting of a stochastic delay competitive Lotka–Volterra model with Lévy jumps. Under some simple assumptions, the sufficient conditions for extinction and stable in the time average of each species are established. The stability in distribution of this model is proved under our assumptions. Finally, the sufficient and necessary criteria for the existence of optimal harvesting policy are established and the explicit expression of the optimal harvesting effort and the maximum of sustainable yield are also obtained. And some numerical simulations are introduced to demonstrate the theoretical results. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, an almost periodic system of impulsive differential equations used in modeling two-species in competition is considered. By the comparison between the solutions of impulsive system and the corresponding non-impulsive system and constructing Lyapunov function, sufficient conditions ensuring the uniformly asymptotic stability of a unique positive almost periodic solution of the system are derived. Finally, an example and its corresponding numerical simulations are presented to explain our theoretical results. [Copyright &y& Elsevier]

Abstract: The effect of toxicants on ecological systems is an important issue from mathematical and experimental points of view. In this paper, we have studied the dynamical behaviours of a two-species competitive system affected by toxic substances. Boundedness, local and global stabilities are addressed. We have also studied the stability of this system with diffusion around the non-trivial stable (in the deterministic case) equilibrium point in a random environment. Extensive numerical simulations are performed using analytical results for a hypothetical set of parameter values. [Copyright &y& Elsevier]