珊瑚礁生态系统的建模与分析
发布时间：2019-04-10 17:25
【摘要】：本文主要研究由珊瑚、海藻、食草鱼和食肉鱼类所组成的珊瑚礁生态系统,通过分析它们之间的关系,我们建立了三个模型.第一个模型主要讨论了大型食肉鱼、食草鱼、人类对两种鱼类的捕捞的相互关联和影响,其中的创新性体现在对食草鱼按年龄或体积大小进行分类,针对某些参数取值范围所得结论与发表在SCIENCE的文献[P.Mumby,etc 40]数据吻合;第二个模型主要讨论两种食草鱼与海藻之间的关系,其中定居鱼(Damselfish)与海藻是互利共生关系,鹦嘴鱼(Parrotfish)与海藻是捕食者和被捕食者关系,而定居鱼与鹦嘴鱼是竞争关系,该模型的创新性体现在第一次把定居鱼的作用考虑到珊瑚礁生态系统中,而大量实验数据表明定居鱼对保持藻类的多样性起到至关重要的作用,所以我们的模型能更好反应珊瑚礁生态系统的实际情况,接着我们对模型的动力学行为(正不变性、有界性、不动点的稳定性及其分支等)进行了详细研究并对给定参数后的系统做了数值模拟;第三个模型继续讨论海藻-定居鱼-鹦嘴鱼的关系,不同之处在于我们用May在1976年提出的协作模型来反映海藻与定居鱼的协作关系,我们对系统的动力学行为进行了详细研究并做了数值模拟.论文所用数学工具主要包括Hartman-Grobman定理、Routh-Hurwitz定理和Sotomayor不动点分支定理.
[Abstract]:In this paper, the coral reef ecosystem consisting of coral, seaweed, grass carp and carnivorous fish is studied. By analyzing the relationship between them, we have established three models of coral reef ecosystem, which are composed of coral, seaweed, grass carp and carnivorous fish. The first model focuses on the interlinkages and impacts of large carnivorous fish, grass carp and humans on the fishing of two species of fish, the innovation of which is the classification of grass carp by age or size. The results obtained according to the range of some parameters agree with the data published in SCIENCE [P. Mumby, etc 40]. The second model mainly discusses the relationship between two species of grass carp and seaweed, in which settled fish (Damselfish) and seaweed are mutually beneficial symbiosis, parrotfish (Parrotfish) and seaweed are predators and arrested predators, and settled fish and parrotfish are competitive. The innovation of the model is that, for the first time, the role of settled fish is taken into account in coral reef ecosystems, and a large number of experimental data show that settled fish play a vital role in maintaining the diversity of algae. So our model is better able to reflect the actual situation of coral reef ecosystems, and then we look at the dynamic behavior of the model (positive invariance, boundedness, The stability of fixed point and its bifurcation are studied in detail, and the numerical simulation of the system with given parameters is carried out. The third model continues to discuss the relationship between algae, settled fish and parrotfish. The difference is that we use the collaboration model proposed by May in 1976 to reflect the collaboration between algae and settled fish. The dynamic behavior of the system is studied in detail and numerically simulated. The mathematical tools used in this paper include Hartman-Grobman theorem, Routh-Hurwitz theorem and Sotomayor fixed point bifurcation theorem.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
本文编号：2455985
[Abstract]:In this paper, the coral reef ecosystem consisting of coral, seaweed, grass carp and carnivorous fish is studied. By analyzing the relationship between them, we have established three models of coral reef ecosystem, which are composed of coral, seaweed, grass carp and carnivorous fish. The first model focuses on the interlinkages and impacts of large carnivorous fish, grass carp and humans on the fishing of two species of fish, the innovation of which is the classification of grass carp by age or size. The results obtained according to the range of some parameters agree with the data published in SCIENCE [P. Mumby, etc 40]. The second model mainly discusses the relationship between two species of grass carp and seaweed, in which settled fish (Damselfish) and seaweed are mutually beneficial symbiosis, parrotfish (Parrotfish) and seaweed are predators and arrested predators, and settled fish and parrotfish are competitive. The innovation of the model is that, for the first time, the role of settled fish is taken into account in coral reef ecosystems, and a large number of experimental data show that settled fish play a vital role in maintaining the diversity of algae. So our model is better able to reflect the actual situation of coral reef ecosystems, and then we look at the dynamic behavior of the model (positive invariance, boundedness, The stability of fixed point and its bifurcation are studied in detail, and the numerical simulation of the system with given parameters is carried out. The third model continues to discuss the relationship between algae, settled fish and parrotfish. The difference is that we use the collaboration model proposed by May in 1976 to reflect the collaboration between algae and settled fish. The dynamic behavior of the system is studied in detail and numerically simulated. The mathematical tools used in this paper include Hartman-Grobman theorem, Routh-Hurwitz theorem and Sotomayor fixed point bifurcation theorem.
【学位授予单位】：上海师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O175
【参考文献】
相关期刊论文 前1条
1 陈兰荪;刘平舟;肖藻;;种群生态系统的持续生存[J];生物数学学报;1988年01期
，本文编号：2455985
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