两性种群动力学模型论文.pdf

两性种群动力学模型摘要学科专业:应用数学研究方向:生物数学指导教师:王稳地研究生;张天然(2002360) 在一些种群中,由于各种各样的原因,雌雄两性的生理特征具有明显的不同, 这些特征主要表现为出生率、死亡率,竞争食物的能力以及逃避被捕食(或危险) (两性数量之比)的变化,. 本文第二章引入了一个类似于Malthus指数增长规律的模型,此模型可以存在一个全局稳定的两性指数解,但是种群的性比是趋向稳定的;第三章在第二章的模型的基础上建立了密度制约的两性模型,得出了种群生命力最强时出生率与死亡率的比例关系,说明l:1的出生率并不一定是最佳的,同时,此模型的性比也是趋于稳定的. ,, 没有偏食的捕食不会改变食饵的性比,即使食饵是周期性振荡的;但是偏食却可以改变食饵的性比,会使性比随着食饵数量的振荡而振荡. 第五章建立了竞争的两性模型,第一个种群具有两性差异,,那么种群一的性比是一个不依赖于竞争系数的常数,只和种群一的出生率和死亡率有关; 数值模拟表明,种群二对种群一中两性的竞争系数的变化对种群一的性比的改变起到了重要的作用. 关键词:两性模型;随机配对;密度制约;年龄结构;性比;捕食;竞争 Population Dynamics ofTwo-Sex ModeIs Abstract Major: Applied mathematics Speciali坷I Biolo#{cal mathem02ics Supervisor Wendi Author Zhang Tianran(20023fiO) Due some ,thephysiology characteristics two Sex subrIopulations of some populations are characteristics mainly ale death rate,birth theability peting forfood and avoiding being predated, may cause alterations ofthe numbers oftwo sex subpopulations and ofsexration(the ratio ofnumber offemale subpopulation thatofmalesubpopulation),However,appropriate sex ratio very important forpopulation ,it much importance theory and practice study two-sex models. In thesecond chapter,a model similar Malthus analogy introduced,which supports an exponential solution which globally asymptotically stable;however,the sex ratio thethird chapter we propose adensity-restricting two-sex model based on the one thesecond chapter and obtain theproportion birth rates and death rates when thesurvival ability most strong,which shows that thetwo-sex birth rate not bestwhen l: addition,the sex ratio Intheforth chapter we propose apredator-prey model withsexdifference prey shown thatthepredation ofprey which not sex-biased not alter theproportion male prey fem818 prey thou曲the number prey population changes