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具有捕食者迁入的一致分数阶食饵-捕食者系统的动力学分析与最优捕获

Dynamical analysis and optimal harvesting of conformable fractional prey-predator system with predator immigration.

作者信息

Kaviya R, Muthukumar P

机构信息

Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), Gandhigram, Tamil Nadu 624 302 India.

出版信息

Eur Phys J Plus. 2021;136(5):542. doi: 10.1140/epjp/s13360-021-01559-w. Epub 2021 May 16.

DOI:10.1140/epjp/s13360-021-01559-w
PMID:34026401
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC8126181/
Abstract

Aim of this work is to study the four species various fractional-order prey-predator or Lotka-Volterra (LV) system with both immigration and harvesting effects. The existence and uniqueness, uniform boundedness, persistence, permanence, and extinction of this system solution are analyzed. The stability behavior of the system is obtained with the help of the Routh-Hurwitz (RH) stability criterion. The small changes in fractional-order values can produce a significant impact on the stability of the system is confirmed. This work verifies that the small amount of immigration effect can change the dynamic nature of the LV system. Numerical results are given to illustrate the obtained theoretical results of the stability analysis. The bionomic equilibrium points of the system are attained with their feasibility conditions. To get the optimal amount of harvesting effect with the Pontryagin's maximum principle, the harvesting parameter is considered as the control parameter.

摘要

这项工作的目的是研究具有迁入和收获效应的四种不同分数阶捕食-食饵或洛特卡-沃尔泰拉（LV）系统。分析了该系统解的存在唯一性、一致有界性、持久性、永久性和灭绝性。借助劳斯-赫尔维茨（RH）稳定性判据获得了系统的稳定性行为。证实了分数阶值的微小变化会对系统的稳定性产生显著影响。这项工作验证了少量的迁入效应可以改变LV系统的动态性质。给出了数值结果以说明稳定性分析所得到的理论结果。得到了系统的生物经济平衡点及其可行性条件。为了用庞特里亚金极大值原理获得最优收获效应，将收获参数视为控制参数。

https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4d83/8126181/d8becd793762/13360_2021_1559_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4d83/8126181/fb7b49e9c494/13360_2021_1559_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4d83/8126181/39e0b47a2fb4/13360_2021_1559_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4d83/8126181/f6c3aff81eec/13360_2021_1559_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4d83/8126181/8280952d4c34/13360_2021_1559_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4d83/8126181/d8becd793762/13360_2021_1559_Fig8_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4d83/8126181/fb7b49e9c494/13360_2021_1559_Fig1_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4d83/8126181/39e0b47a2fb4/13360_2021_1559_Fig2_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4d83/8126181/f6c3aff81eec/13360_2021_1559_Fig4_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4d83/8126181/8280952d4c34/13360_2021_1559_Fig6_HTML.jpg
https://cdn.ncbi.nlm.nih.gov/pmc/blobs/4d83/8126181/d8becd793762/13360_2021_1559_Fig8_HTML.jpg

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本文引用的文献

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