DYNAMIC ANALYSIS AND OPTIMAL CONTROL OF A FRACTIONAL ORDER SINGULAR LESLIE-GOWER PREY-PREDATOR MODEL

doi:10.1007/s10473-020-0520-z

数学物理学报(英文版) ›› 2020, Vol. 40 ›› Issue (5): 1525-1552.doi: 10.1007/s10473-020-0520-z

DYNAMIC ANALYSIS AND OPTIMAL CONTROL OF A FRACTIONAL ORDER SINGULAR LESLIE-GOWER PREY-PREDATOR MODEL

马琳洁^1,2, 刘斌^1,2

1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China;
2. Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China

收稿日期:2018-09-17 修回日期:2019-09-30 出版日期:2020-10-25 发布日期:2020-11-04
通讯作者: Bin LIU E-mail:binliu@mail.hust.edu.cn
作者简介:Linjie MA,E-mail:mlj0314@126.com
基金资助:
This work was partially supported by NNSFC (11971185).

DYNAMIC ANALYSIS AND OPTIMAL CONTROL OF A FRACTIONAL ORDER SINGULAR LESLIE-GOWER PREY-PREDATOR MODEL

Linjie MA^1,2, Bin LIU^1,2

1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China;
2. Hubei Key Laboratory of Engineering Modeling and Scientific Computing, Huazhong University of Science and Technology, Wuhan 430074, China

Received:2018-09-17 Revised:2019-09-30 Online:2020-10-25 Published:2020-11-04
Contact: Bin LIU E-mail:binliu@mail.hust.edu.cn
Supported by:
This work was partially supported by NNSFC (11971185).

摘要/Abstract

摘要： In this article, we investigate a fractional-order singular Leslie-Gower prey-predator bioeconomic model, which describes the interaction between populations of prey and predator, and takes into account the economic interest. We firstly obtain the solvability condition and the stability of the model system, and discuss the singularity induced bifurcation phenomenon. Next, we introduce a state feedback controller to eliminate the singularity induced bifurcation phenomenon, and discuss the optimal control problems. Finally, numerical solutions and their simulations are considered in order to illustrate the theoretical results and reveal the more complex dynamical behavior.

关键词: fractional order system, differential-algebraic system, prey-predator bioeconomic model, singularity induced bifurcation, optimal control

Abstract: In this article, we investigate a fractional-order singular Leslie-Gower prey-predator bioeconomic model, which describes the interaction between populations of prey and predator, and takes into account the economic interest. We firstly obtain the solvability condition and the stability of the model system, and discuss the singularity induced bifurcation phenomenon. Next, we introduce a state feedback controller to eliminate the singularity induced bifurcation phenomenon, and discuss the optimal control problems. Finally, numerical solutions and their simulations are considered in order to illustrate the theoretical results and reveal the more complex dynamical behavior.

Key words: fractional order system, differential-algebraic system, prey-predator bioeconomic model, singularity induced bifurcation, optimal control

中图分类号:

34A08

马琳洁, 刘斌. DYNAMIC ANALYSIS AND OPTIMAL CONTROL OF A FRACTIONAL ORDER SINGULAR LESLIE-GOWER PREY-PREDATOR MODEL[J]. 数学物理学报(英文版), 2020, 40(5): 1525-1552.

Linjie MA, Bin LIU. DYNAMIC ANALYSIS AND OPTIMAL CONTROL OF A FRACTIONAL ORDER SINGULAR LESLIE-GOWER PREY-PREDATOR MODEL[J]. Acta mathematica scientia,Series B, 2020, 40(5): 1525-1552.

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DYNAMIC ANALYSIS AND OPTIMAL CONTROL OF A FRACTIONAL ORDER SINGULAR LESLIE-GOWER PREY-PREDATOR MODEL

DYNAMIC ANALYSIS AND OPTIMAL CONTROL OF A FRACTIONAL ORDER SINGULAR LESLIE-GOWER PREY-PREDATOR MODEL

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