期刊
INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS
卷 20, 期 4, 页码 1209-1219出版社
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218127410026411
关键词
Chaos; fractional-order calculus; simplified Lorenz system; time-domain methods; bifurcations
资金
- National Nature Science Foundation of People's Republic of China [60672041]
- National Science Foundation for Post-doctoral Scientists of People's Republic of China [20070420774]
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.
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