https://doi.org/10.1140/epjp/i2016-16254-8
Regular Article
Dynamical properties and complexity in fractional-order diffusionless Lorenz system
1
School of Physics and Electronics, Central South University, 410083, Changsha, China
2
Institute for Mathematical Research, Universiti Putra Malaysia, Serdang, Malaysia
3
Malaysia-Italy Centre of Excellence for Mathematical Science, Universiti Putra Malaysia, Serdang, Malaysia
* e-mail: kehui@csu.edu.cn
Received:
11
May
2016
Revised:
21
June
2016
Accepted:
26
June
2016
Published online:
4
August
2016
In this paper, dynamics and complexity of the fractional-order diffusionless Lorenz system which is solved by the developed discrete Adomian decomposition method are investigated numerically. Dynamical properties of the fractional-order diffusionless Lorenz system with the control parameter and derivative order varying is analyzed by using bifurcation diagrams, and period-doubling route to chaos in different cases is observed. The complexity of the system is investigated by means of Lyapunov characteristic exponents, multi-scale spectral entropy algorithm and multiscale Renyi permutation entropy algorithm. It can be observed that the three methods illustrate consistent results and the system has rich complex dynamics. Interestingly, complexity decreases with the increase of derivative order. It shows that the fractional-order diffusionless Lorenz system is a good model for real applications such as information encryption and secure communication.
© Società Italiana di Fisica and Springer-Verlag Berlin Heidelberg, 2016
