捕食者-被捕者中含有化学计量学的离散型模型

A Discrete Predator-prey Model with Stoichiometric Factor

大部分捕食者-被捕者模型是连续的,但是生物的发展未必是连续的,而且环境变化对生物的作用普遍存在时滞性.根据连续系统考虑的捕食者和被捕者的相互作用、Beverton-Holt差分方程以及化学计量学因素对系统的影响,建立了离散的捕食者-被捕者模型.分析表明:新建立的模型,基本上保留了连续系统的基本特征,揭示了能量富足的矛盾.进一步通过对全局的吸引集的构造,对模型的动力学行为有深刻的认识,还指出了生物灭绝和濒临灭绝的差别,这表明新模型比连续系统和直接利用连续解的离散方法得到的离散模型包含更多的生物意义.

Most of predator-prey systems are continuous; but the growth of organisms is not necessarily continuous and the effect of the environmental change is not instantaneous, either. Having considered the interaction between the predator and the prey in continuous system, Beverton-Holt equation and the influence of the stoichiometric factor to the system, we construct predator-prey model. The analysis shows that they retain most of the fundamental features of the continuous model and also reveal the paradox of energy; Also analytical and numerical analyses of the model provide more insight into system dynamics including a set of global attraction, meanwhile we notes the fine distinctions between the two states of organisms--facing to die out and having died out, which indicate that it contains more biologic phenomena than continuous model and discrete one deduced from continuous one by using the continuous solution discretely.