毒素影响下具有阶段结构的种群动力学行为研究

发布时间：2018-07-29 08:12

【摘要】：众所周知,科学技术突飞猛进不但提高了经济的发展而且提高了人类生活的水准,但是环境问题却变得严峻。特别是随着工业生产的快速发展,进一步加剧了环境的污染,如果不采取及时有效的措施,生物种群的生存环境将会受到严重的影响。种群生态学对人们的日常生产实践具有重要的指导作用以及现实意义。特别是随着环境的日益恶化,许多人对于种群在污染环境下生存状况的研究一直是热点问题。然而许多种群模型的研究仅仅考虑把种群的成长过程看成一个整体,这是不合理的。一方面：种群个体的每一个生命阶段表现出的生理功能差异比较明显；另一方面：不同阶段的种群之间在生存时相互有影响。以上两方面对种群的生存状况具有重要的影响。因此,研究种群模型有必要考虑其生理阶段的存在。所以,对于环境污染下的种群生存状况研究,就需要我们通过建立合理的生物数学模型,并对种群模型进行定性分析,预测种群在环境污染下的发展变化,这样不仅可以制定相应的环保措施使得种群可以持续生存,还对保持生态种群丰富的多样性具有重要意义。论文的主要内容结构有以下几个部分构成：绪论第一章：预备知识。第二章：考虑了单种群两阶段(成年、幼年)的生物种群模型,其中成年和幼年种群同时受毒素影响。借助常微分方程相关理论方法,证明种群模型解有界、正平衡点和原点的稳定性,然后给出了种群持续生存、灭绝的条件,又证明了种群模型有周期解并且是稳定,最后运用Matlab数值模拟证明了相关结论。第三章：考虑了具有种间相互作用的单种群两阶段生物种群模型,而且它们同时受毒素作用,证明了正解的有界性,平衡点的存在性和稳定性,获得了种群灭绝、生存的条件,同时考虑了周期解的相关结果。并数值模拟验证本章的结论。第四章：考虑了毒素影响下食饵-捕食数学模型(食饵是具有阶段结构,捕食种群仅捕食幼年种群),得到了系统解的有界性,系统持久性的条件,并给出了系统周期解的存在性和稳定性,最后通过数值模拟进一步证明了文中的相关结论。第五章：考虑毒素作用下种群模型具有阶段性和自食(捕食种群有阶段性且自食),探讨了食饵一捕食者模型持续生存问题以及周期解的相关结果,最后通过数值模拟进一步证明了本章中的相关结论。最后,主要对论文进行小结并提出未来需要进一步讨论的方向；致谢；参考文献等。
[Abstract]:As we all know, the rapid development of science and technology has not only improved the economic development but also improved the standard of human life, but the environmental problems have become serious. Especially with the rapid development of industrial production, the pollution of the environment is further aggravated. If no timely and effective measures are taken, the living environment of the biological population will be seriously affected. Population ecology plays an important role in guiding people's daily production practice as well as practical significance. Especially with the deterioration of the environment, many people's research on the survival of the population in the polluted environment has been a hot issue. However, it is unreasonable for many population models to consider the population growth process as a whole. On the one hand, the difference of physiological function in each stage of the population is obvious; on the other hand, the different stages of the population affect each other in survival. The above two aspects have an important effect on the survival of the population. Therefore, it is necessary to consider the existence of physiological stage in the study of population model. Therefore, for the study of population survival under environmental pollution, we need to establish a reasonable biological mathematical model and qualitatively analyze the population model to predict the population development and change under environmental pollution. In this way, not only can the corresponding environmental protection measures be formulated to make the population survive sustainably, but also it is of great significance to maintain the rich diversity of the ecological population. The main content structure of the thesis has the following parts: the first chapter: preparatory knowledge. In chapter 2, a two-stage biological population model is considered, in which both adult and juvenile populations are affected by toxins. With the help of the theory of ordinary differential equation, it is proved that the solution of population model is bounded, and the stability of positive equilibrium point and origin point is proved. Then, the conditions of population survival and extinction are given, and it is proved that the population model has periodic solution and is stable. Finally, Matlab numerical simulation is used to prove the relevant conclusions. In chapter 3, the two-stage population model of single population with interspecific interaction is considered, and they are simultaneously affected by toxins. The boundedness of positive solution, the existence and stability of equilibrium point are proved, and the conditions for population extinction and survival are obtained. At the same time, we consider the results of periodic solutions. The conclusion of this chapter is verified by numerical simulation. In chapter 4, the predator-prey mathematical model under the influence of toxin is considered. The boundedness of the system solution and the condition of the persistence of the system are obtained. The existence and stability of the periodic solution of the system are given, and the relevant conclusions are further proved by numerical simulation. Chapter 5: considering that the population model has stages and self-feeding (prey population has stage and self-feeding) under the action of toxin, the problem of persistent survival of predator-prey model and the results of periodic solution are discussed. Finally, the relevant conclusions in this chapter are further proved by numerical simulation. Finally, the paper is summarized and the future direction of further discussion is put forward; thanks; references, etc.
【学位授予单位】：兰州交通大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O175

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