Stability and non-standard finite difference method of the generalized Chua's circuit

被引：47

作者：

Radwan, A. G. ^{[1
,2
]}

Moaddy, K. ^{[3
]}

Momani, Shaher ^{[4
]}

机构：

[1] KAUST, Dept Elect Engn, Thuwal, Saudi Arabia

[2] Cairo Univ, Fac Engn, Dept Engn Math, Cairo, Egypt

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

[4] Univ Jordan, Dept Math, Fac Sci, Amman 11942, Jordan

来源：

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

关键词：

Fractional differential equations; Non-standard finite difference schemes; Chaotic systems; Chua's circuit; Memristor; EQUATIONS;

D O I：

10.1016/j.camwa.2011.04.047

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we develop a framework to obtain approximate numerical solutions of the fractional-order Chua's circuit with Memristor using a non-standard finite difference method. Chaotic response is obtained with fractional-order elements as well as integer-order elements. Stability analysis and the condition of oscillation for the integer-order system are discussed. In addition, the stability analyses for different fractional-order cases are investigated showing a great sensitivity to small order changes indicating the poles' locations inside the physical s-plane. The Grunwald-Letnikov method is used to approximate the fractional derivatives. Numerical results are presented graphically and reveal that the non-standard finite difference scheme is an effective and convenient method to solve fractional-order chaotic systems, and to validate their stability. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：961 / 970

页数：10

共 27 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]

Bohannan G., 2006, US patent, Patent No. 20060267595

[6] MEMRISTOR - MISSING CIRCUIT ELEMENT [J].

CHUA, LO .

IEEE TRANSACTIONS ON CIRCUIT THEORY, 1971, CT18 (05) :507-+

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

Diethelm, K ;

Ford, NJ .

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

[8] Numerical Bifurcation of Predator-Prey Fractional Differential Equations with a Constant Rate Harvesting [J].

Erjaee, G. H. .

ISND 2007: PROCEEDINGS OF THE 2007 INTERNATIONAL SYMPOSIUM ON NONLINEAR DYNAMICS, PTS 1-4, 2008, 96

[9] An analytical expression for the input impedance of a fractal tree obtained by a microelectronical process and experimental measurements of its non-integral dimension [J].

Haba, T. Cisse ;

Loum, Georges L. ;

Ablart, G. .

CHAOS SOLITONS & FRACTALS, 2007, 33 (02) :364-373

[10]

Hussian G, 2008, P 8 SEM DIFF EQ DYN

← 1 2 3 →