论文标题
新型Predator-Prey模型，可以准确分析解决方案
Novel predator-prey model admitting exact analytical solution
论文作者
论文摘要
Lotka-Volterra Predator-Prey模型仍然代表描述人口动态竞争的范式。尽管它极为简单，但它不承认分析解决方案，因此，通常采用数值整合方法将其应用于科学的各个领域。本工作的目的是调查具有共享标准Lotka-Volterra模型的广泛特征的新捕食者模型的存在，同时提供了拥有精确的分析解决方案的优势。为此，已经开发了第一步。在上述模型类别中，唯一具有承认简单精确分析解决方案的属性的现有模型。根据已知的基本功能，明确获得了该特殊的捕食者 - 纯模型的解决方案，并研究了其主要属性。最后，考虑了基于强力竞争概念的概括，及其扩展到$ n $组成的竞争系统。
The Lotka-Volterra predator-prey model still represents the paradigm for the description of the competition in population dynamics. Despite its extreme simplicity, it does not admit an analytical solution, and for this reason, numerical integration methods are usually adopted to apply it to various fields of science. The aim of the present work is to investigate the existence of new predator-prey models sharing the broad features of the standard Lotka-Volterra model and, at the same time, offer the advantage of possessing exact analytical solutions. To this purpose, a general Hamiltonian formalism, which is suitable for treating a large class of predator-prey models in population dynamics within the same framework, has been developed as a first step. The only existing model having the property of admitting a simple exact analytical solution, is identified within the above class of models. The solution of this special predator-prey model is obtained explicitly, in terms of known elementary functions, and its main properties are studied. Finally, the generalization of this model, based on the concept of power-law competition, as well as its extension to the case of $N$-component competition systems, are considered.
