涉及Holling III型功能反应的额外食物捕食系统的随机最优和时间最优控制研究

Daliparthi Bhanu Prakash, D. Vamsi
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引用次数: 2

摘要

摘要本文对一个耦合的非线性动力系统进行了详细而新颖的随机最优控制分析。状态方程被建模为一个额外的食物提供的捕食者-捕食者系统,该系统对捕食者具有Holling III型功能反应和捕食者之间的特异内竞争。我们首先将最优控制问题讨论为具有线性二次控制的拉格朗日问题。其次,我们考虑时间最优控制设置中的最优控制问题。我们首先建立了这两个问题的最优控制的存在性,然后使用随机最大值原理来刻画这些最优控制。为了实现理论发现,基于随机前向后向扫描方法进行了进一步的数值模拟。在生物保护和害虫管理的背景下讨论了在这些最优控制问题中获得的结果。
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Stochastic optimal and time-optimal control studies for additional food provided prey–predator systems involving Holling type III functional response
Abstract This article consists of a detailed and novel stochastic optimal control analysis of a coupled non-linear dynamical system. The state equations are modelled as an additional food-provided prey–predator system with Holling type III functional response for predator and intra-specific competition among predators. We first discuss the optimal control problem as a Lagrangian problem with a linear quadratic control. Second, we consider an optimal control problem in the time-optimal control setting. We initially establish the existence of optimal controls for both these problems and later characterize these optimal controls using the Stochastic maximum principle. Further numerical simulations are performed based on stochastic forward-backward sweep methods for realizing the theoretical findings. The results obtained in these optimal control problems are discussed in the context of biological conservation and pest management.
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来源期刊
Computational and Mathematical Biophysics
Computational and Mathematical Biophysics Mathematics-Mathematical Physics
CiteScore
2.50
自引率
0.00%
发文量
8
审稿时长
30 weeks
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