Multi-Scroll Chaotic System Based on Even-Symmetric Step-Wave Sequence Control

Abstract:

This paper presents a new approach for generating multi-scroll chaotic attractors. First, a new double scroll chaotic system with piecewise linearity and invariance under the transformationis introduced. Then, by using the even-symmetric step-wave sequence switching control method in this system to extend the number of saddle-focus points of index 2, the intended multi-scroll chaotic attractors can be obtained. A circuit for generating multi-scroll chaotic attractors is designed, and the experimental results are also given, confirming the consistency of the theory design and circuit implementation.

• Periodical: Applied Mechanics and Materials (Volume 340)
• Pages: 760-766
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.340.760
• Online since: July 2013
• Authors: Zi Long Tang, Si Min Yu
• Keywords: Circuit Implementation, Even-Symmetric Step-Wave Sequence, Multi-Scroll Chaotic Attractor, Switching Control

References

[1] Lü J H, Chen G R (2006) Generating multiscroll chaotic attractors, Theories, methods and applications, Int. J. Bifurc. Chaos 116(7): 775-858.

DOI: 10.1142/s0218127406015179

[2] Chua L O, Komuro M, Matsumoto T (1986) The double scroll family, IEEE Trans. Circuits Syst. I 33(7): 1073-1117.

DOI: 10.1109/tcs.1986.1085869

[3] Suykens J A K, Vandewalle J (1991) Quasilinear approach to nonlinear systems and the design of n-double scroll (n = 1; 2; 3; 4; . . . ), G, IEE Proc 138(4): 595-603.

DOI: 10.1049/ip-g-2.1991.0098

[4] Elwakil A S, Özoguz S (2006) Multiscroll chaotic oscillators: the nonautonomous approach, IEEE Trans. Circuits Syst 153(7): 862-866.

DOI: 10.1109/tcsii.2006.880032

[5] Tang K S, Zhong G Q, Chen G R, Man K F (2001) Generation of n−scroll attractors via sine function, IEEE Trans. Circuits Syst 48(2): 1369-1372.

DOI: 10.1109/81.964432

[6] Zhong G Q, Man K F, Chen G R (2002) A systematic approach to generating n−scroll attractors, Int. J. Bifurc. Chaos 12(7): 2907-2915.

DOI: 10.1142/s0218127402006230

[7] Yalcin M E, Suykens J A K, Vandewalle J (2000) Experimental confirmation of 3- and 5-scroll attractors from a generalized Chua's circuit, IEEE Trans. Circuits Syst 47(5): 425-429.

DOI: 10.1109/81.841929

[8] Yalcin M E, Suykens J A K, Vandewalle J (2002) Families of scroll grid attractors, Int. J. Bifurc. Chaos 112(7): 23-41.

DOI: 10.1142/s0218127402004164

[9] Lü J H, Zhou T, Chen G R, Yang X (2002) Generating chaos with a switching piecewise-linear controller, Chaos 112(5): 344-349.

DOI: 10.1063/1.1478079

[10] Lü J H, Han F, Yu X, Chen G (2004) Generating 3-D multi-scroll chaotic attractors: A hysteresis series switching method, Automatica 40(5): 1677-1687.

DOI: 10.1016/j.automatica.2004.06.001

[11] Yu S M, Lü J H, Leung H, Chen G R (2005) Design and implementation of n-scroll chaotic attractors from a general Jerk circuit, IEEE Transactions on Circuits 52(8): 1459-1476.

DOI: 10.1109/tcsi.2005.851717

[12] Yu S M, Tang K S, Chen G R (2007) "Generation of n×m-scroll attractors under a Chua-circuit framework, Int. J. Bifurc. Chaos 17(5): 3951-3964.

DOI: 10.1142/s0218127407019809

[13] Yu S M, Lü J H, Chen G R, Yu X H (2012) Design and implementation of grid multiwing hyperchaotic Lorenz system family via switching control and constructing super-heteroclinic loops., IEEE Transactions on Circuits Syst 34(8): 1015-1028.

DOI: 10.1109/tcsi.2011.2180429