随机生态模型的应用研究

发布时间：2018-03-14 13:02

本文选题：随机干扰　切入点：平均持续生存　出处：《集美大学》2017年硕士论文　论文类型：学位论文

【摘要】：在现实生态系统中,生物间的活动总伴随着各种随机干扰,为了更加全面地描述客观实际,随机生态模型的应用研究愈来愈重要.目前随机生态模型在种群动力学,流行病学等领域得到了广泛的发展与应用.本文主要分三部分研究如下三类随机生态模型的动力学行为:第一部分研究了具有负面效应的随机浮游动植物模型.通过构造比较系统证明了全局正解的存在唯一性、均值有界性.接着得到了系统灭绝的充分条件,研究了随机系统在对应确定性系统正平衡点处的渐近行为.最后,用数值模验证了理论结果的正确性.第二部分研究了具有食饵染病和修正Leslie-Gower项的随机捕食食饵模型.对于确定性系统,证明了正平衡点的局部渐近稳定性;对于随机系统,首先用It?o公式和随机理论证明了系统全局正解的存在唯一性,其次给出了系统灭绝和强平均持续生存的充分条件,接着证明了在一定的条件下,系统存在唯一的平稳分布.最后用数值模拟验证了理论结果的正确性.第三部分研究了周期脉冲投放病毒的随机害虫治理模型.先证明了系统解的均值有界性和害虫灭绝周期解的全局吸引性,接着讨论了系统的灭绝性并得到系统非平均持续生存的阈值.最后利用数值模拟验证了计算结果的正确性并丰富了所得理论结果.
[Abstract]:In the reality of ecological system, the biological activities of the total accompanied by various disturbances, to a more comprehensive description of the objective reality, and application of stochastic ecological model more important. At present the random ecological models in population dynamics, epidemiology and other fields has been widely development and application. The dynamic behavior of this paper is divided into three parts as follows three stochastic ecological model: the first part of the study has a negative effect of the random plankton model. By constructing the comparison system to prove the existence and uniqueness of global positive solutions, mean boundedness. Then the sufficient condition of the system of extinction obtained, study the asymptotic behavior in the corresponding deterministic system at the positive equilibrium point of the stochastic system. Finally, the numerical model to verify the correctness of the theoretical results. The second part studies the stochastic predator-prey model with disease in the prey and modified Leslie-Gower items Type. For deterministic systems, local asymptotic stability of the positive equilibrium is proved; for stochastic systems, the first It? O equation and the stochastic theory to prove the existence and uniqueness of positive solutions of the whole system, then gives the sufficient condition for system extinction and strong persistence in the mean, then proves that under certain conditions, the stationary distribution only exists in the system. Finally the simulation verify the correctness of the theoretical results by numerical simulation. The third part studies the stochastic model of pest control on virus cycle pulse. First prove that the mean system global boundedness and pest extinction cycle solution of attraction, then discussed the extinction of the system and the non average persistence of the threshold system. Finally using numerical simulation to verify the correctness of the calculation results and enrich the theoretical results.

【学位授予单位】：集美大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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