Analytic left inversion of multivariable Lotka-Volterra models
Analytic left inversion of multivariable Lotka-Volterra models
复制标题
多变量 Lotka-Volterra 模型的解析左反演
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
K. Ebrahimi
中科院分区：
文献类型：
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作者：
W. Gray;Luis A. Duffaut Espinosa;K. Ebrahimi
人们对管理作为人类重要食物来源的动物种群有着极大的兴趣。Lotka-Volterra系统是一个经典的种群模型，它以时变参数为输入，种群水平为输出，可以看作是一个非线性的输入-输出系统。如果这些输入中的一些可以被驱动，这就建立了一个开环控制问题，其中需要一个特定的人口曲线作为时间的函数，目标是确定合适的系统输入来产生这个曲线。数学上，这是一个左反转问题。本文利用组合Hopf代数的概念，求解了可表示为Chen-Fliess级数的多变量输入-输出系统的一般左逆问题。然后将该方法应用于三种、两输入、两输出的Lotka-Volterra系统。生物学目标是改变食物链中顶级捕食者物种的种群动态，以防止灭绝。
There is great interest in managing populations of animal species that are vital food sources for humans. A classical population model is the Lotka-Volterra system, which can be viewed as a nonlinear input-output system when time-varying parameters are taken as inputs and the population levels are the outputs. If some of these inputs can be actuated, this sets up an open-loop control problem where a certain population profile as a function of time is desired, and the objective is to determine suitable system inputs to produce this profile. Mathematically, this is a left inversion problem. In this paper, the general left inversion problem is solved for multivariable input-output systems that can be represented in terms of Chen-Fliess series using concepts from combinatorial Hopf algebras. The method is then applied to a three species, two-input, two-output Lotka-Volterra system. The biological goal is to change the population dynamics of the top-level predator species in a food chain in order to prevent extinction.