Yuan Sanling, Ji Xuehui, Zhu Huaiping
College of Science, Shanghai University for Science and Technology, Shanghai 200093, China email:
College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China email:
Math Biosci Eng. 2017;14(5-6):1477-1498. doi: 10.3934/mbe.2017077.
In this paper, we investigate the dynamics of a delayed logistic model with both impulsive and stochastic perturbations. The impulse is introduced at fixed moments and the stochastic perturbation is of white noise type which is assumed to be proportional to the population density. We start with the existence and uniqueness of the positive solution of the model, then establish sufficient conditions ensuring its global attractivity. By using the theory of integral Markov semigroups, we further derive sufficient conditions for the existence of the stationary distribution of the system. Finally, we perform the extinction analysis of the model. Numerical simulations illustrate the obtained theoretical results.
在本文中，我们研究了一个具有脉冲和随机扰动的时滞逻辑模型的动力学。脉冲在固定时刻引入，随机扰动为白噪声类型，假设其与种群密度成正比。我们首先研究模型正解的存在性和唯一性，然后建立确保其全局吸引性的充分条件。通过使用积分马尔可夫半群理论，我们进一步推导系统平稳分布存在的充分条件。最后，我们对模型进行灭绝分析。数值模拟验证了所得的理论结果。
