Venturino Ezio
Dipartimento di Matematica, Università di Torino, via Carlo Alberto 10, 10123 Torino, Italy.
IMA J Math Appl Med Biol. 2002 Sep;19(3):185-205.
The author has recently proposed and investigated models for the study of interacting species subject to an additional factor, a disease spreading among one of them, that somehow affects the other one. The inadequacy of such a model comes from the basic assumption on the interacting species. It is well known that the cycles found in the Lotka-Volterra system exhibit a neutral stability, and this phenomenon is carried over to the proposed model. Here we would like to extend the study to account for population dynamics leading to carrying capacities, i.e. logistic behaviour. This corresponds to the so-called quadratic predator-prey models found in the literature. We are able to show that in some cases the trajectories are bounded, and also analyse the local stability of some equilibria.
作者最近提出并研究了一些模型，用于研究受附加因素影响的相互作用物种，该附加因素是一种在其中一个物种中传播的疾病，它以某种方式影响另一个物种。这种模型的不足之处源于对相互作用物种的基本假设。众所周知，在洛特卡 - 沃尔泰拉系统中发现的周期表现出中性稳定性，并且这种现象延续到了所提出的模型中。在这里，我们希望扩展研究，以考虑导致承载能力的种群动态，即逻辑斯谛行为。这对应于文献中发现的所谓二次捕食者 - 猎物模型。我们能够证明在某些情况下轨迹是有界的，并且还分析了一些平衡点的局部稳定性。
