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Control Chaos in Hindmarsh--Rose Neuron by Using Intermittent Feedback with One Variable |
| MA Jun1,2, WANG Qing-Yun3, JIN Wu-Yin4, XIA Ya-Feng1 |
| 1School of Science, Lanzhou University of Technology, Lanzhou 7300502Department of Physics, Central China Normal University, Wuhan 4300793Department of Mathematics, Inner Mongolia Finance and Economics College, Huhhot 0100514College of Mechano-Electronic Engineering, Lanzhou University of Technology, Lanzhou 730050 |
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| Cite this article: |
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MA Jun, WANG Qing-Yun, JIN Wu-Yin et al 2008 Chin. Phys. Lett. 25 3582-3585 |
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Abstract The mechanism of the famous phase compression is discussed, and it is used to control the chaos in the Hindmarsh--Rose (H-R) model. It is numerically confirmed that the phase compression scheme can be understood as one kind of intermittent feedback scheme, which requires appropriate thresholds and feedback coefficient, and the intermittent feedback can be realized with the Heaviside function. In the case of control chaos, the output variable (usually the voltage or the membrane potential of the neuron) is sampled and compared with the external standard signal of the electric electrode. The error between the sampled variable and the external standard signal of the electrode is input into the system only when the sampled variable surpasses the selected thresholds. The numerical simulation results confirm that the chaotic H-R system can be controlled to reach arbitrary n-periodical (n=1, 2, 3, 4, 5, 6, ...) orbit or stable state even when just one variable is feed backed into the system intermittently. The chaotic Chua circuit is also investigated to check its model independence and effectiveness of the schemes and the equivalence of the two schemes are confirmed again.
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05.45.-a
05.45.Xt
87.17.Nn
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Received: 10 June 2008
Published: 26 September 2008
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[1] Ott E et al 1990 Phys. Rev. Lett. 64 1196
[2] Boccaletti S et al 2000 Phys. Rep. 329 103
[3] Ma J et al 2005 Acta. Phys. Sin. 54 4602 (inChinese)
[4] Gao J H, Zheng Z G 2007 Chin. Phys. Lett. 24359
[5]Zhan M et al 2000 Chin. Phys. Lett. 17 332
[6] Yang J Z and Zhang M 2005 Chin. Phys. Lett. 222183
[7] Sun F Y 2006 Chin. Phys. Lett. 23 32
[8] Zheng Y H et al 2006 Chin. Phys. Lett. 23 3176
[9] Shen J H et al 2006 Chin. Phys. Lett. 23 1406
[10] Luo X S 1999 Acta Phys. Sin. 48 402 (inChinese)
[11] Zhang X et al 2001 Acta. Phys. Sin. 50 624(in Chinese)
[12] Zhang X and Shen K 2001 Phys. Rev. E 63046212
[13] Corron N J et al 2000 Phys. Rev. Lett. 843835
[14] Hindmarsh J L and Rose R M 1982 Nature 276162
[15] Hindmarsh J L et al 1984 Proc. R. Soc. London B 221 87
[16] Wang H X et al 2005 Chin. Phys. Lett. 22 2173
[17] Shi X and Lu Q S 2004 Chin. Phys. Lett. 211695
[18] Jr R E et al 2006 Phys. Rev. E 74 061906
[19] Wu Y et al 2007 Chin. Phys. Lett. 24 3066
[20] Shi X and Lu Q S 2007 Chin. Phys. Lett. 24636
[21] Belykh I et al 2005 Phys. Rev. Lett. 94188101
[22] Madan R N 1993 Chua's Circuit: A Paradigm for Chaos(Singapore: World Scientific)
[23] Ma J, Jia Y and Yi M et al 2008 Chaos, Solitons{\rm\& Fractals (in press)(http://dx.doi.org/10.1016/j.chaos.2008.05.014) |
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