Share This Article:

Controlling Unstable Discrete Chaos and Hyperchaos Systems

DOI: 10.4236/am.2013.411A2001    3,480 Downloads   4,879 Views   Citations
Author(s)    Leave a comment

ABSTRACT

A method is introduced to stabilize unstable discrete systems, which does not require any adjustable control parameters of the system. 2-dimension discrete Fold system and 3-dimension discrete hyperchaotic system are stabilized to fixed points respectively. Numerical simulations are then provided to show the effectiveness and feasibility of the proposed chaos and hyperchaos controlling scheme.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

X. Li and S. Qian, "Controlling Unstable Discrete Chaos and Hyperchaos Systems," Applied Mathematics, Vol. 4 No. 11B, 2013, pp. 1-6. doi: 10.4236/am.2013.411A2001.

References

[1] E. Ott, C. Grebogi and J. A. York, “Controlling Chaos,” Physical Review Letters, Vol. 64, No. 11, 1990, pp. 11961199.
[2] D. Liu, L. Liu and Y. Yang, “H∞ Control of DiscreteTime Singularly Perturbed Systems via Static Output Feedback,” Abstract and Applied Analysis, Vol. 2013, 2013, Article ID: 528695.
[3] Z. Wang, H. T. Zhao and X. Y. Kong, “Delayed Feedback Control and Bifurcation Analysis of an Autonomy System,” Abstract and Applied Analysis, Vol. 2013, 2013, Article ID: 167065.
[4] G. R. Chen and J. H. LU, “Dynamic Analysis, Control and Synchronization of Lorenz System,” Science Publishing Company, Beijing, 2003.
[5] B. Peng, V. Petro and K. Showalter, “Controlling Chemical Chaos,” The Journal of Physical Chemistry, Vol. 95, No. 13, 1991, pp. 4957-4961.
http://dx.doi.org/10.1021/j100166a013
[6] H. Salarieh and A. Alasty, “Control of Stochastic Chaos Using Sliding Mode Method,” Journal of Computational and Applied Mathematics, Vol. 225, No. 1, 2009, pp. 135-145.
http://dx.doi.org/10.1016/j.cam.2008.07.032
[7] K. Pyragas, “Continuous Control of Chaos by Self-Controlling Systems,” Physical Letter A, Vol. 170, No. 6, 1992, pp. 421-428.
http://dx.doi.org/10.1016/0375-9601(92)90745-8
[8] E. H. Abed, H. O. Wang and R. C. Chen, “Stabilization of Period Doubling Bifurcations and Implications for Control of Chaos,” Physica D, Vol. 70, No. 1-2, 1994, pp. 154-164.
http://dx.doi.org/10.1016/0167-2789(94)90062-0
[9] K. A. Mirus and J. C. Sprott, “Controlling Chaos in Lowand High-Dimensional Systems with Periodic Parametric Perturbations,” Physical Review E, Vol. 59, No. 5, 1999, pp. 5313-5324.
http://dx.doi.org/10.1103/PhysRevE.59.5313
[10] X. Li, Y. Chen and Z. B. Li, “Function Projective Synchronization of Discrete-Time Chaotic Systems,” Zeitschrift für Naturforschung Section A—A Journal of Physical Scienses, Vol. 63, No. 1-2, 2008, pp. 7-14.
[11] L. Yang, Z. R. Liu and J. M. Mao, “Controlling Hyperchaos,” Physical Review Letters, Vol. 84, No. 1, 2000, pp. 67-70. http://dx.doi.org/10.1103/PhysRevLett.84.67
[12] S. L. Bu, S. Q. Wang and H. Q. Ye, “Stabilizing Unstable Discrete Systems,” Physical Review E, Vol. 64, 2001, Article ID: 046209.
[13] X. Li and Y. Chen, “Stabilizing of Two-Dimensional Discrete Lorenz Chaotic System and Three-Dimensional Discrete Rossler Hyperchaotic System,” Chinese Physics Letters, Vol. 26, No. 9, 2009, Article ID: 090503.
[14] M. Itoh, T. Yang and L. O. Chua, “Conditions for Impulsive Synchronization of Chaotic and Hyperchaotic Systems,” International Journal of Bifurcation and Chaos, Vol. 11, No. 2, 2001, pp. 551-560.
http://dx.doi.org/10.1142/S0218127401002262
[15] X. Y. Wang, “Chaos in Complex Nonlinear Systems,” Publishing House of Electronics Industry, Beijing, 2003.

  
comments powered by Disqus

Copyright © 2018 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.