两类具有双时滞的捕食—食饵模型的局部稳定性和Hopf分岔

发布时间：2018-02-02 13:59

本文关键词： Hopf分岔双时滞率依赖功能反应函数　出处：《江苏大学》2017年硕士论文　论文类型：学位论文

【摘要】：生态系统具有复杂性和多样性,对应的种群生态系统模型具有着丰富动力学性质,因而探究种群生态系统理论中的奥秘已成为当下的热点研究课题之一。值得一提的是,由于诸如多时滞、率依赖等影响因素广泛存在于种群生态系统,因此考虑这些因素能够更加贴切的描述自然生态系统的真实状态。基于此背景,本文重点讨论了两类含多时滞的捕食-食饵模型的动力学特征及其性质。首先,本文对国内外的研究现状作了调查并进行归纳整理,给出了选题的背景及意义。其次,重点探究了含率依赖、反馈和妊娠时滞的HollingIII功能反应函数生态传染病系统模型。在系统中将两个时滞项看作分岔参数,深入地讨论了该模型正平衡点的稳定性,并且应用Hopf分岔理论,给出了平衡点处发生Hopf分岔的条件。运用动力学理论得到了系统的分岔方向和相应的周期解,最后模拟验证了本文的结论。接下来,研究了带有阶段结构、功能反应函数、选择收获时滞以及避难时滞的捕食-食饵系统模型。同样地,结合稳定性理论和分岔理论探究了该模型的分岔条件及周期解,与之前不考虑食饵避难因素的模型相比,此模型更具有避免食饵灭绝的现实意义,数据模拟验证理论分析的正确性。最后,系统的总结了论文的研究工作,同时指出了本文需要改进之处,并对今后进一步的研究目标及方向作出展望。
[Abstract]:The ecosystem is complex and diverse, and the corresponding population ecosystem model has rich dynamic properties. Therefore, exploring the mystery of population ecosystem theory has become one of the hot research topics. It is worth mentioning that, because of such factors as multi-delay, rate-dependent and other factors widely exist in the population ecosystem. Therefore, considering these factors can more accurately describe the real state of the natural ecosystem. Based on this background, this paper focuses on the dynamic characteristics and properties of two kinds of predator-prey models with multiple delays. In this paper, the current research situation at home and abroad has been investigated and summarized, and the background and significance of the topic have been given. Secondly, the emphasis has been put on the research of percentage dependence. The HollingIII functional response function Eco-infectious system model with feedback and pregnancy delay is presented. The stability of the positive equilibrium point of the model is discussed in depth by considering the two time-delay terms as bifurcation parameters in the system. By using the Hopf bifurcation theory, the condition of Hopf bifurcation at the equilibrium point is given, and the bifurcation direction and the corresponding periodic solution are obtained by using the dynamics theory. Finally, the conclusion of this paper is verified by simulation. Then, the predator-prey system model with stage structure, functional response function, harvest delay and asylum delay is studied. Combined with the stability theory and bifurcation theory, the bifurcation conditions and periodic solutions of the model are explored. Compared with the previous model, which does not consider the factors of prey refuge, the model has more practical significance of avoiding prey extinction. Data simulation verifies the correctness of the theoretical analysis. Finally, the paper summarizes the research work, points out that this paper needs improvement, and makes a prospect for the future research goal and direction.
【学位授予单位】：江苏大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175

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