【作者】 谢丛波；

【导师】 范猛；

【作者基本信息】 东北师范大学 ， 应用数学， 2005， 硕士

【副题名】两种捕食者能够共存于同一种食饵

【摘要】 生物化学计量学即研究生态系统中能量与多种化学元素平衡的问题。近十几年来,人们正在把这种研究方法引入到生物动力系统中,文献[2]以生物化学计量学原理为基础建立连续模型,证明了两种捕食者能够于同一种食饵——这在竞争排斥原理(认为n个种群不能共存于少于n的资源)看来是不可能的结论,却可以在一定程度上对自然界中生物多样性现象给予解释,但我们必须注意到,连续模型本身会限制许多复杂现象的产生,如混沌——即使在简单的一维离散系统中都可能出现;此外,实验中数据的采集都是离散的;许多生物种群世代是不重叠的事实也不容忽视,基于上述原因,本文将建立以生物化学计量学原理为基础的离散模型,考虑两种元素碳(C)和磷(P),研究食物质量对系统的影响,从理论上证明两种捕食者仍然可以共存于同一种食饵,并利用大量的数值模拟与连续模型进行比较,生动的展示了更符合实际的复杂的生物动力学现象(比如从倍周期分叉到混沌),希望这些结论能够对解决实际问题,特别是保护和维持生物多样性提供一些理论依据。更多还原

【Abstract】 Biological stoichiometry is the study of the balance of energy and multiple chemical elements in biological systems. In the last decade, it has been introduced into biodynamics system and promoted new dynamic behaviors and insights. Loladze, et al (2004), by constructing continurous models, have testified that a stable equilibrium is possible with two predators on one prey, and offered an explanation for the phenomenons of coexistence or biodiversity in a sense, which is impossible in the opinion of the competitive exclusion principle (CEP). However, we note that continuous model itself mathematically preclude any possibility of chaos, but even one dimensional discrete systems can potentially exhibit it. In addition, the data for experiments are collected on discrete time intervals and many species have no over-lap whatsoever between successive generations. All these call for discrete model. We will construct the analogical discrete model, by capturing two essential elements C and P, investigate how the food quality effects the system. The paper will show that not only the coexistence is possible for two predators on one prey, but more intriguing and profound scenario can occur in the discrete model, such as through the periodic doubling route to chaos if the parameters chosen suitably. We hope that the theoretic analysis can offer a little help to mankind to understand, study, protect and maintain biodiversity, as far as in our lies.更多还原