BIFURCATIONS AND CHAOS IN FRACTIONAL-ORDER SIMPLIFIED LORENZ SYSTEM

被引：82

作者：

Sun, Kehui ^{[1
]}

Wang, Xia ^{[1
]}

Sprott, J. C. ^{[2
]}

机构：

[1] Cent South Univ, Sch Phys Sci & Technol, Changsha 410083, Peoples R China

[2] Univ Wisconsin, Dept Phys, Madison, WI 53706 USA

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2010年 / 20卷 / 04期

基金：

美国国家科学基金会;

关键词：

Chaos; fractional-order calculus; simplified Lorenz system; time-domain methods; bifurcations; FREQUENCY-DOMAIN APPROXIMATION; PREDICTOR-CORRECTOR APPROACH;

D O I：

10.1142/S0218127410026411

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The dynamics of fractional-order systems have attracted increasing attention in recent years. In this paper, we numerically study the bifurcations and chaotic behaviors in the fractional-order simplified Lorenz system using the time-domain scheme. Chaos does exist in this system for a wide range of fractional orders, both less than and greater than three. Complex dynamics with interesting characteristics are presented by means of phase portraits, bifurcation diagrams and the largest Lyapunov exponent. Both the system parameter and the fractional order can be taken as bifurcation parameters, and the range of existing chaos is different for different parameters. The lowest order we found for this system to yield chaos is 2.62.

引用

页码：1209 / 1219

页数：11

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