Approximations of chaotic attractors and its circuit design based on the parameter switching algorithm

Luo Shao-Xuan; He Bo-Xia; Qiao Ai-Min; Wang Yan-Chun

doi:10.7498/aps.64.200508

Abstract

Based on the parameter switching algorithm and the discrete chaotic system, a new chaotic system based parameter switching algorithm is proposed. The principles of parameter switching algorithm and chaotic system based parameter switching algorithm are presented in detail by means of flow chart and step description. By applying phase diagram observation method, chaotic attractor approximation of the unified chaotic system is investigated based on parameter switching algorithm and chaotic system based parameter switching algorithm. It shows that chaos can be obtained by switching two periodic parameters and periodic state can be observed by switching two chaotic parameters. Thus the formulas chaos+ chaos = periodic and period+ period = chaos are proved to be workable in this paper. Chaotic attractor approximation of Rössler chaotic system is also studied by employing the two switching methods. Two cases are investigated. Firstly, a chaotic switching system is obtained by switching a chaotic parameter and a periodic parameter. Then a more complex switching scheme is carried out. Periodic system is switched by two periodic parameters and a chaotic parameter. So, the formulas chaos+ periodic = chaos and periodic+ period+ chaos = periodic are proved to be workable. It shows that the switching system is the approximation of the original system under specified parameter, and the attractor is in accordance with the attractor of the targeting system. The outputs of the Logistic map based parameter switching algorithm are more complex than those of existing parameter switching algorithm. As the distribution of logistic map is not uniform, the approximate attractor does not consist of the targeting system and shows more complicated structure. But approximate attractors can be obtained when the distribution of discrete sequence is uniform. In addition, the chaotic map based parameter switching algorithm has larger secret key space since it has the initial values and parameter of the chaotic map. Finally, the parameter switching circuit of Rössler system is designed by introducing a square wave generator. Compared with the traditional switching chaotic circuit (switching between different systems), the design of parameter switch circuit is simpler as it does not need to change the original structure of the system. The output is affected by the frequency of the square wave. By adding an appropriate frequency square wave generator, the circuit simulation agrees with the numerical simulation. It presents a theoretical and experimental base for the practical application of the parameter switching chaotic systems.

Keywords:

Authors and contacts

1.
Mechanical and Electronic Engineering Department, Bengbu College, Bengbu 233030, China;
2.
Nanjing University of Science and Technology, Nanjing 210094, China
Funds: Project supported by the National Natural Science Foundation of China (Grant No. 51175276), the Key Program of the Natural Science Foundation of the Higher Education Institutions of Anhui Province, China (Grant No. KJ2013Z193), and the Foundation for Outstanding Young Teachers in University of Anhui Province, China (Grant No. 2012SQRL212).

References

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Cited By

[1]	Duan S M, Wu G Z 2013 Appl. Mech. Mater. 392 232
[2]	Xiao X, Zhou L, Zhang Z 2014 Commun. Nonl. Sci. Num. Simul. 19 2039
[3]	Wang Z, Huang X, Li Y X 2013 Chin. Phys. B 22 010504
[4]	Jamal S S, Shah T, Hussain I 2013 Nonl. Dyn. 73 1469
[5]	Zhang Y, Chen T L 2006 J. Electr. Sci. Tech. 34 763 (in Chinese) [张勇, 陈天麒 2006 电子科技大学学报 34 763]
[6]	Corporation H P 2014 J. Nonl. Dyn. 2014 918586
[7]	Sun C C, Xu Q C, Ying S 2013 Chin. Phys. B 22 030507
[8]	Liu Y Z, Jiang C S, Ling C S 2007 Acta Phys. Sin. 56 3107 (in Chinese) [刘扬正, 姜长生, 林长圣 2007 56 3107]
[9]	Liu Y Z, Jiang C S, Ling C S 2007 Acta Phys. Sin. 56 707 (in Chinese) [刘扬正, 姜长生, 林长圣 2007 56 707]
[10]	Qi A, Han C, Wang G 2010 Communications, Circuits and Systems (ICCCAS) International Conference on. IEEE 2010 p417
[11]	Chen Z Y, Xue Z H, Zhang C 2014 Acta Phys. Sin. 63 010504 (in Chinese) [陈章耀, 雪增红, 张春 2014 63 010504]
[12]	Almeida J, Peralta-Salas D, Romera M 2005 Physica D 200 124
[13]	Danca M F 2013 Commu. Nonl. Sci. Num. Simul. 18 500
[14]	Danca M F, Romera M, Pastor G 2012 Nonl. Dyn. 67 2317
[15]	Mao Y, Tang W K S, Danca M 2010 Appl. Math. Comp. 217 355
[16]	Foias C, Jolly M S 1995 Nonlinearity 8 295
[17]	Lu J, Wu X, Han X, L J 2004 Phys. Lett. A 329 327
[18]	Rössler O E 1976 Phys. Lett. A 57 397

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Catalog

Vol. 64, Issue 20 - 2015-10-20

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