Due to human-caused deforestation,global warming,and other environmental factors,habitat fragmentation became widespread.This fragmentation has a variety of detrimental repercussions for many species as well as humans...Due to human-caused deforestation,global warming,and other environmental factors,habitat fragmentation became widespread.This fragmentation has a variety of detrimental repercussions for many species as well as humans,especially in the agricultural economy.It causes insect outbreaks,the expansion of alien species,and disrupts biological management by rendering the habitat unsuitable for natural enemies in agriculture.Providing natural enemies with additional food is one method to improve the ecosystem and support them.In this study,we assumed that the ecosystem is separated into two patches and that predators can easily migrate from one patch to the next,while prey stays inside its patch's territory.We looked at the impact of offering more food to predators in a patchy environment using dynamical systems theory.The permanence,stability,and various bifurcations that occur in the system are studied using a rigorous mathematical analysis.The study looks at how predator's access to other food sources affects pest management.By adjusting the provided food's characteristic qualities,such as(nutritional)quality and quantity,one can limit and manage the pest in one or both patches,as well as eliminate predators from the ecosystem.This research reveals that providing predators with additional food(of specified quality and quantity)can help in controlling chaotic behavior in the system.The findings of the study are supported by numerical simulations.展开更多
本文是关于动态域上不连续动力系统理论进展的一个综述.笔者给出了具边界转换的不连续动力系统和具时间切换的不连续动力系统的基本概念;提出了不连续动力系统的两个特征:其一是所考虑的不连续动力系统具有随时间变化的定义域.其二是所...本文是关于动态域上不连续动力系统理论进展的一个综述.笔者给出了具边界转换的不连续动力系统和具时间切换的不连续动力系统的基本概念;提出了不连续动力系统的两个特征:其一是所考虑的不连续动力系统具有随时间变化的定义域.其二是所考虑的不连续动力系统具有关于边界或切换时刻的不连续性.由此自然提出了关于动态域上不连续动力系统的动力学问题,包括流的奇异性规律、周期运动特性、转换分支性态及复杂动力学等.笔者着重介绍了近年逐渐形成的动态域上不连续动力系统理论(2005年由Luo A C J提出):首先纵览不连续动力系统研究所经历的三次发展浪潮,致力于展现该理论形成的历史过程;接着勾画出该理论的基本架构,即以不连续动力系统流转换理论和映射动力学为基本内容,并由其自然派生拓展出不连续动力系统转换分支理论、流障碍理论、多值向量场理论等.动态域上不连续动力系统理论的关键之处在于:受物理能量层启发,针对不连续动力系统动边界提出了“G函数”的核心概念.G函数实质上是借助极限工具在动边界任一点局部给出一种度量方法,从而使得精细研究动态边界上流的转换成为可能.本文还介绍了关于不连续动力系统研究的一些新进展.展开更多
文摘Due to human-caused deforestation,global warming,and other environmental factors,habitat fragmentation became widespread.This fragmentation has a variety of detrimental repercussions for many species as well as humans,especially in the agricultural economy.It causes insect outbreaks,the expansion of alien species,and disrupts biological management by rendering the habitat unsuitable for natural enemies in agriculture.Providing natural enemies with additional food is one method to improve the ecosystem and support them.In this study,we assumed that the ecosystem is separated into two patches and that predators can easily migrate from one patch to the next,while prey stays inside its patch's territory.We looked at the impact of offering more food to predators in a patchy environment using dynamical systems theory.The permanence,stability,and various bifurcations that occur in the system are studied using a rigorous mathematical analysis.The study looks at how predator's access to other food sources affects pest management.By adjusting the provided food's characteristic qualities,such as(nutritional)quality and quantity,one can limit and manage the pest in one or both patches,as well as eliminate predators from the ecosystem.This research reveals that providing predators with additional food(of specified quality and quantity)can help in controlling chaotic behavior in the system.The findings of the study are supported by numerical simulations.
文摘本文是关于动态域上不连续动力系统理论进展的一个综述.笔者给出了具边界转换的不连续动力系统和具时间切换的不连续动力系统的基本概念;提出了不连续动力系统的两个特征:其一是所考虑的不连续动力系统具有随时间变化的定义域.其二是所考虑的不连续动力系统具有关于边界或切换时刻的不连续性.由此自然提出了关于动态域上不连续动力系统的动力学问题,包括流的奇异性规律、周期运动特性、转换分支性态及复杂动力学等.笔者着重介绍了近年逐渐形成的动态域上不连续动力系统理论(2005年由Luo A C J提出):首先纵览不连续动力系统研究所经历的三次发展浪潮,致力于展现该理论形成的历史过程;接着勾画出该理论的基本架构,即以不连续动力系统流转换理论和映射动力学为基本内容,并由其自然派生拓展出不连续动力系统转换分支理论、流障碍理论、多值向量场理论等.动态域上不连续动力系统理论的关键之处在于:受物理能量层启发,针对不连续动力系统动边界提出了“G函数”的核心概念.G函数实质上是借助极限工具在动边界任一点局部给出一种度量方法,从而使得精细研究动态边界上流的转换成为可能.本文还介绍了关于不连续动力系统研究的一些新进展.
