Hybrid tactics for bifurcation control in a fractional-order delayed predator-prey model

被引：38

作者：

Zhou, Weigang ^{[1
]}

Huang, Chengdai ^{[1
]}

Xiao, Min ^{[2
]}

Cao, Jinde ^{[3
,4
]}

机构：

[1] Hubei Univ Arts & Sci, Sch Math & Stat, Xiangyang 441053, Peoples R China

[2] Nanjing Univ Posts & Telecommun, Coll Automat, Nanjing 210003, Jiangsu, Peoples R China

[3] Southeast Univ, Res Ctr Complex Syst & Network Sci, Nanjing 210096, Jiangsu, Peoples R China

[4] Southeast Univ, Sch Math, Nanjing 210096, Jiangsu, Peoples R China

来源：

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS | 2019年 / 515卷

关键词：

Hopf bifurcation; Hybrid control; Fractional-order; Delayed predator-prey system; TIME-DELAY; STABILITY; SYSTEM;

D O I：

10.1016/j.physa.2018.09.185

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

This paper handles the problem of controlling bifurcation for a fractional delayed predator prey system via active hybrid control strategy. Delay-induced bifurcation conditions of the Hopf bifurcation are achieved for controlled model by using time delay as a bifurcation parameter. It is illustrated that the stability performance is drastically enhanced with the help of the proposed controller, yet Hopf bifurcation emerges in advance if the controller is removed. Finally, numerical simulations are carried out to confirm our theoretical analysis. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：183 / 191

页数：9

共 30 条

[1] A multiple phenotype predator-prey model with mutation [J].

Abernethy, Gavin M. ;

Mullan, Rory ;

Glass, David H. ;

McCartney, Mark .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2017, 465 :762-774

[2]

Bhalekar S., 2011, J. Fract. Calc. Appl., V1, P1, DOI DOI 10.1155/2011/250763

[3] Patterns formations in a diffusive ratio-dependent predator-prey model of interacting populations [J].

Camara, B. I. ;

Hague, M. ;

Mokrani, H. .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2016, 461 :374-383

[4]

Custis T, 2015, J DRUGS DERMATOL, V14, P1200

[5] Control of a fractional-order economical system via sliding mode [J].

Dadras, Sara ;

Momeni, Hamid Reza .

PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2010, 389 (12) :2434-2442

[6]

Deng WH, 2007, NONLINEAR DYNAM, V48, P409, DOI [10.1007/s11071-006-9094-0, 10.1007/s11071 -006-9094-0]

[7] Dynamical behaviors of fractional-order Lotka–Volterra predator–prey model and its discretization [J].

Elsadany A.A. ;

Matouk A.E. .

Journal of Applied Mathematics and Computing, 2015, 49 (1-2) :269-283

[8] Effect of time delay on a harvested predator-prey model [J].

Gazi N.H. ;

Bandyopadhyay M. .

Journal of Applied Mathematics and Computing, 2008, 26 (1-2) :263-280

[9] On the existence of positive solutions and negative solutions of singular fractional differential equations via global bifurcation techniques [J].

Guan, Yongliang ;

Zhao, Zengqin ;

Lin, Xiuli .

BOUNDARY VALUE PROBLEMS, 2016,

[10] THEORY OF ROTATED EQUATIONS AND APPLICATIONS TO A POPULATION MODEL [J].

Han, Maoan ;

Hou, Xiaoyan ;

Sheng, Lijuan ;

Wang, Chaoyang .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2018, 38 (04) :2171-2185

← 1 2 3 →