论文标题
在周期性环境中具有退化权重的一类捕食者捕集模型的次谐波解决方案
Subharmonic solutions for a class of predator-prey models with degenerate weights in periodic environments
论文作者
论文摘要
本文介绍了具有周期性系数的一类平面汉密尔顿系统的亚谐波解决方案的存在，多样性，最小的复杂性和全球结构，这是V. Volterra的经典捕食者模型，其最具范式的示例。通过基于全球分叉理论的技术的拓扑方法，本文的第一部分确定了它们的性质，多样性和最小的复杂性，以及它们的全球最小结构，以模型设置的函数系数的配置。本文的第二部分介绍了一种动力学系统方法，该方法基于拓扑马术的理论，该理论允许检测除次谐波解决方案外，``混乱型''solutions''。作为我们分析的副产品，周期性环境中最简单的捕食者 - 捕集原型模型可以引起混乱的动力学。由于最大原理施加的顺序，这不能在合作和准合作动力学中发生。
This paper deals with the existence, multiplicity, minimal complexity and global structure of the subharmonic solutions to a class of planar Hamiltonian systems with periodic coefficients, being the classical predator-prey model of V. Volterra its most paradigmatic example. By means of a topological approach based on techniques from global bifurcation theory, the first part of the paper ascertains their nature, multiplicity and minimal complexity, as well as their global minimal structure, in terms of the configuration of the function coefficients in the setting of the model. The second part of the paper introduces a dynamical system approach based on the theory of topological horseshoes that permits to detect, besides subharmonic solutions, ``chaotic-type'' solutions. As a byproduct of our analysis, the simplest predator-prey prototype models in periodic environments can provoke chaotic dynamics. This cannot occur in cooperative and quasi-cooperative dynamics, as a consequence of the ordering imposed by the maximum principle.
