On stability, persistence, and Hopf bifurcation in fractional order dynamical systems

被引：0
作者：
H. A. El-Saka
E. Ahmed
M. I. Shehata
A. M. A. El-Sayed
机构：
[1] Mansoura University,Mathematics Department, Faculty of Science
[2] Mansoura University,Mathematics Department, Faculty of Science
[3] Alexandria University,Mathematics Department, Faculty of Science
来源：
Nonlinear Dynamics | 2009年 / 56卷
关键词：
Fractional order; Bifurcation;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This is a preliminary study about the bifurcation phenomenon in fractional order dynamical systems. Persistence of some continuous time fractional order differential equations is studied. A numerical example for Hopf-type bifurcation in a fractional order system is given, hence we propose a modification of the conditions of Hopf bifurcation. Local stability of some biologically motivated functional equations is investigated.
引用
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页码：121 / 126
页数：5
相关论文
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[1]  
Ahmed E.(2005)Numerical solution for the fractional replicator equation Int. J. Mod. Phys. 16 1-9
[2]  
El-Sayed A.M.A.(2006)On some Routh-Hurwitz conditions for fractional order differential equations and their applications in Lorenz, Rossler, Chua and Chen systems Phys. Lett. A 358 1-553
[3]  
El-Mesiry E.M.(2006)On some Routh-Hurwitz conditions for fractional order differential equations and their applications in Lorenz, Rossler, Chua and Chen systems Phys. Lett. A 358 1-22
[4]  
El-Saka H.A.A.(2007)Equilibrium points, stability and numerical solutions of fractional-order predator-prey and rabies models J. Math. Anal. Appl. 325 542-52
[5]  
Ahmed E.(2002)A predictor–corrector approach for the numerical solution of fractional differential equations Nonlinear Dyn. 29 3-699
[6]  
El-Sayed A.(2004)Detailed error analysis for a fractional Adams method Numer. Algorithms 36 31-54
[7]  
El-Saka H.(2005)Numerical methods for multi-term fractional (arbitrary) orders differential equations Appl. Math. Comput. 160 683-823
[8]  
Ahmed E.(2004)Numerical solution for multi-term fractional (arbitrary) orders differential equations Comput. Appl. Math. 23 33-undefined
[9]  
El-Sayed A.M.A.(2007)On the fractional-order logistic equation Appl. Math. Lett. 20 817-undefined
[10]  
El-Saka H.A.A.(1999)Fractional calculus and the evolution of fractal phenomena Physica A 265 535-undefined
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