Zhu Fang Fang, Meng Xin Zhu, Zhang Tong Hua
College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, PR China.
Department of Mathematics, Swinburne University of Technology, Hawthorn, VIC 3122 Australia.
Math Biosci Eng. 2019 Feb 26;16(3):1554-1574. doi: 10.3934/mbe.2019074.
In this study, we propose an n-species stochastic model which considers the influences of the competitions and delayed diffusions among populations on dynamics of species. We then investigate the stochastic dynamics of the model, such as the persistence in mean of the species, and the asymptotic stability in distribution of the model. Then, by using the Hessian matrix and theory of optimal harvesting, we investigate the optimal harvesting problem, obtaining the optimal harvesting effort and the maximum of expectation of sustainable yield (ESY). Finally, we numerically discuss some examples to illustrate our theoretical findings, and conclude our study by a brief discussion.
在本研究中，我们提出了一个(n)物种随机模型，该模型考虑了种群之间的竞争和时滞扩散对物种动态的影响。然后，我们研究了该模型的随机动力学，例如物种的均值持久性以及模型分布的渐近稳定性。接着，通过使用黑塞矩阵和最优收获理论，我们研究了最优收获问题，得到了最优收获努力量和可持续产量期望值（ESY）的最大值。最后，我们通过数值讨论一些例子来说明我们的理论结果，并通过简要讨论总结我们的研究。
