2009
DOI: 10.1016/j.chaos.2009.03.016
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Dynamic analysis of a fractional-order Lorenz chaotic system☆

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Cited by 168 publications
(78 citation statements)
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“…It has attracted many investigators [1][2]. Many famous fractional order systems, such as Rōssler system, Lorenz system, Chua's circuit, Duffing system and so on, have been studied [3][4][5][6][7][8][9]. In view of the fact that fractional calculus provides another good way to describe, predict and control physical systems accurately, it has been applied to control system, physics and system modeling [10][11][12][13][14].…”
Section: Introductionmentioning
confidence: 99%
“…It has attracted many investigators [1][2]. Many famous fractional order systems, such as Rōssler system, Lorenz system, Chua's circuit, Duffing system and so on, have been studied [3][4][5][6][7][8][9]. In view of the fact that fractional calculus provides another good way to describe, predict and control physical systems accurately, it has been applied to control system, physics and system modeling [10][11][12][13][14].…”
Section: Introductionmentioning
confidence: 99%
“…It is worth mentioning that higher-dimensional chaotic systems with more than one positive Lyapunov exponent can indeed show more complex dynamics. It has been recently demonstrated that many fractional-order systems can display chaotic (or hyperchaotic) behaviours such as: fractional-order Duffing system [7], fractionalorder Chua's system [8], fractional-order Lorenz system [9], fractional-order Chen system [10], fractional-order Rössler system [11], fractional-order Liu system [12], fractional-order Arneodo system [13].…”
Section: Introductionmentioning
confidence: 99%
“…Systems with fractional-order dynamics were proven to exist in different disciplines [1], such as viscoelastic systems [2], electromagnetic waves [3], dielectric polarization [4], quantitative finance [5], and quantum evolution of complex systems [6]. Chaotic phenomena were found in several fractional-order systems, e.g., the fractional Lorenz system [7,8], the fractional Duffing system [9][10][11], the fractional Chua system [12,13], the fractional Chen system [14,15], the fractional van der Pol system [16,17], and the fractional Newton-Leipnik system [18,19].…”
Section: Introductionmentioning
confidence: 99%