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

作　　者：Linjie MA Bin LIU 马琳洁;刘斌(School of Mathematics and Statistics,Huazhong University of Science and Technology,Wuhan 430074,China;Hubei Key Laboratory of Engineering Modeling and Scientific Computing,Huazhong University of Science and Technology,Wuhan 430074,China)

机构地区：[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

出　　处：《Acta Mathematica Scientia》2020年第5期1525-1552,共28页数学物理学报（B辑英文版）

基　　金：partially supported by NNSFC(11971185).

摘　　要：In this article,we investigate a fractional-order singular Leslie-Gower prey-predator bioeconomic model,which describes the interaction bet ween populations of prey and predator,and takes into account the economic interest.We firstly obtain the solvability condition and the st ability of the model sys tem,and discuss the singularity induced bifurcation phenomenon.Next,we introduce a st ate feedback controller to elimina te 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 

分 类 号：O175[理学—数学] O232[理学—基础数学]