Non-standard finite difference schemes for solving fractional-order Rossler chaotic and hyperchaotic systems

被引：27

作者：

Moaddy, K. ^{[2
]}

Hashim, I. ^{[2
]}

Momani, S. ^{[1
]}

机构：

[1] Univ Jordan, Dept Math, Amman 11942, Jordan

[2] Univ Kebangsaan Malaysia, Sch Math Sci, Ukm Bangi Selangor 43600, Malaysia

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2011年 / 62卷 / 03期

关键词：

Fractional differential equations; Chaos; Non-standard finite deference schemes; Rossler system; ADOMIAN DECOMPOSITION; EQUATIONS;

D O I：

10.1016/j.camwa.2011.03.059

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, the non-standard finite difference method (for short NSFD) is implemented to study the dynamic behaviors in the fractional-order Rossler chaotic and hyperchaotic systems. The Grunwald-Letnikov method is used to approximate the fractional derivatives. We found that the lowest value to have chaos in this system is 2.1 and hyperchaos exists in the fractional-order Rossler system of order as low as 3.8. Numerical results show that the NSFD approach is easy to implement and accurate when applied to differential equations of fractional order. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：1068 / 1074

页数：7

共 30 条

[1]

[Anonymous], 1993, INTRO FRACTIONAL CA

[2]

[Anonymous], 2000, APPL NONSTANDARD FIN

[3]

[Anonymous], 1999, FRACTIONAL DIFFERENT

[4]

BALEANU D., 2009, FRACTIONAL CALCULUS

[5] Series solutions of non-linear Riccati differential equations with fractional order [J].

Cang, Jie ;

Tan, Yue ;

Xu, Hang ;

Liao, Shi-Jun .

CHAOS SOLITONS & FRACTALS, 2009, 40 (01) :1-9

[6] Analysis of fractional differential equations [J].

Diethelm, K ;

Ford, NJ .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2002, 265 (02) :229-248

[7] A predictor-corrector approach for the numerical solution of fractional differential equations [J].

Diethelm, K ;

Ford, NJ ;

Freed, AD .

NONLINEAR DYNAMICS, 2002, 29 (1-4) :3-22

[8]

ERJAEE GH, 2009, J PHYS C SER, V96, P12

[9] Physical interpretation of initial conditions for fractional differential equations with Riemann-Liouville fractional derivatives [J].

Heymans, Nicole ;

Podlubny, Igor .

RHEOLOGICA ACTA, 2006, 45 (05) :765-771

[10]

Hussian G, 2008, P 8 SEM DIFF EQ DYN

← 1 2 3 →