Solution of a new high-performance fractional-order Lorenz system and its dynamics analysis

Recently, fractional calculus theory has been deeply studied, and fractional-order chaotic systems have attracted much attention from scholars because of their rich dynamic properties. In order to make the fractional-order chaotic systems better applied in the field of communication security, it is...

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Veröffentlicht in:Nonlinear dynamics 2023-04, Vol.111 (8), p.7469-7493
Hauptverfasser: Gu, Yujuan, Li, Guodong, Xu, Xiangliang, Song, Xiaoming, Zhong, Huiyan
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Sprache:eng
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Zusammenfassung:Recently, fractional calculus theory has been deeply studied, and fractional-order chaotic systems have attracted much attention from scholars because of their rich dynamic properties. In order to make the fractional-order chaotic systems better applied in the field of communication security, it is necessary to explore the new fractional-order chaotic system with better chaotic characteristics. In this paper, according to the fractional calculus, a new high-performance fractional-order Lorenz system is firstly proposed, and the numerical solution of the system is obtained by the Adomian algorithm. Secondly, the Lyapunov exponent, bifurcation behavior, stability and global dynamics analysis of the system are analyzed. It is found that the system appears limit cycle phenomenon when the parameters take specific values and different simulation steps will affect the chaotic state of the system. In addition, the Simulink model of the new system is established. Then compared with four fractional-order Lorenz systems, the new system has a higher maximum Lyapunov exponent and permutation entropy complexity. Finally, the simulation experiment shows that the new system is better than the classical fractional-order Lorenz chaotic systems in each performance index and it has more complex chaotic behavior, which lays an experimental foundation for the application of communication security.
ISSN:0924-090X
1573-269X
DOI:10.1007/s11071-023-08239-7