A New Five Dimensional Hyperchaotic System and its Fractional Order Form

Ling Liu; Chong Xin Liu; Yi Fan Liao

doi:10.4028/www.scientific.net/AMM.464.375

Paper Titles

A Comparative Study of Global-Best Harmony Search and Bat Algorithms on Optimization Problems
p.352

Mobile Sync Client Design of Cloud Storage System
p.358

PCI Express-Based NVMe Solid State Disk
p.365

Introducing Neural Networks as a Computational Intelligent Technique
p.369

A New Five Dimensional Hyperchaotic System and its Fractional Order Form
p.375

Downlink Outage Probability Analysis of D-MIMO Systems over a Composite Channel
p.381

Study on the Structural Model of Human Pose
p.387

High Quality 3D Restoration of Photographed Structures Using V.R. Technologies
p.391

Rapid Prototyping in Developing Process with CA Systems Application
p.399

HomeApplied Mechanics and MaterialsApplied Mechanics and Materials Vol. 464A New Five Dimensional Hyperchaotic System and its...

A New Five Dimensional Hyperchaotic System and its Fractional Order Form

Abstract:

In this paper, a new five-dimensional hyperchaotic system by introducing two additional states feedback into a three-dimensional smooth chaotic system. With three nonlinearities, this system has more than one positive Lyapunov exponents. Based on the fractional derivative theory, the fractional-order form of this new hyperchaotic system has been investigated. Through predictor-corrector algorithm, the system is proved by numerical simulation analysis. Simulation results are provided to illustrate the performance of the fractional-order hyperchaotic attractors well.

You might also be interested in these eBooks

View Preview

Info:

Periodical:

Applied Mechanics and Materials (Volume 464)

Pages:

375-380

DOI:

https://doi.org/10.4028/www.scientific.net/AMM.464.375

Citation:

Cite this paper

Online since:

November 2013

Authors:

Ling Liu*, Chong Xin Liu, Yi Fan Liao

Keywords:

Fractional Derivative, Fractional-Order Hyperchaos, Hyperchaotic System, Predictor Corrector

Export:

RIS, BibTeX

Price:

Permissions CCC:

Request Permissions

Permissions PLS:

Request Permissions

Сopyright:

Citation:

* - Corresponding Author

References

[1] R. C. Koeller, Application of fractional calculus to the theory of viscoelasticity, Journal of Aookied Mechanics, Vol. 51 (1984), p.299.

Google Scholar

[2] T. T. Hartley, C. F. Lorenzo and H. K. Qammer, Chaos in a fractional order Chua system, IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, Vol. 42 (1995), p.485.

DOI: 10.1109/81.404062

Google Scholar

[3] I. Grigorenko, E. Grigorenko, Chaotic dynamics of the fractional Lorenz system, Physical Review Letters, Vol. 91 (2003), p.034101.

DOI: 10.1103/physrevlett.96.199902

Google Scholar

[4] X. Wang, M. Wang, Dynamic analysis of the fractional-order Liu system and its synchronization, Chaos, Vol. 17 (2007), pp.033106-1.

DOI: 10.1063/1.2755420

Google Scholar

[5] R. J. Lu, C. X. Liu, Realization of fractional-order Liu chaotic system by circuit, Chinese Physics B, Vol. 16 (2007), p.1586.

DOI: 10.1088/1009-1963/16/6/016

Google Scholar

[6] P. W. H. Deng, C. P. Li, The evolution of chaotic dynamics for fractional unified system, Physics Letters A, Vol. 372, p.401.

Google Scholar

[7] C. X. Liu, J. J. Lu, A novel fractional-order hyperchaotic system and its circuit realization, International Journal of Modern Physics B, Vol. 24(10) (2010), p.1299.

DOI: 10.1142/s0217979210053707

Google Scholar

[8] L. Liu, C. X. Liu and Y. B. Zhang, Experimental verification of a four-dimensional Chua's system and its fractional order chaotic attractors, International Journal of Bifurcation and Chaos, Vol. 19 (2009). p.2473.

DOI: 10.1142/s0218127409024256

Google Scholar

[9] L. Liu, D. L. Liang and C. X. Liu, Nonlinear state observer design for projective synchronization of fractional-order permanent magnet synchronous motor, International Journal of Modern Physics B, Vol. 26 (2012). pp.1250166-1.

DOI: 10.1142/s0217979212501664

Google Scholar