Chin. Phys. Lett.  2009, Vol. 26 Issue (5): 050502    DOI: 10.1088/0256-307X/26/5/050502
GENERAL |
State-to-State Transitions in a Hindmarsh-Rose Neuron System
HUANG Shou-Fang, ZHANG Ji-Qian, DING Shi-Jiang
College of Physics and Electronic Information, Anhui Normal University, Wuhu 241000
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HUANG Shou-Fang, ZHANG Ji-Qian, DING Shi-Jiang 2009 Chin. Phys. Lett. 26 050502
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Abstract We investigate the dynamical response of the neuron system to a feeble external signal by using the Hindmarsh-Rose model, when the system is tuned below the first bifurcation point, which corresponds to the period-1 bursting state, and an external signal with a fixed period of about 170s is introduced to the system. It is found that to respond to the outside signal, the system changes from the period-1 state to a period-2 one with variation of the signal amplitude, indicating the occurrence of state-to-state transition (SST). Moreover, when a signal with different fixed periods is introduced, we can also find a similar transition between other states. Furthermore, the effect of the frequency of the signal on the transition is also discussed. These results may imply that SST plays a constructive role in information processing in neuron systems.
Keywords: 05.45.-a      05.45.Df      05.65.+b     
Received: 19 December 2008      Published: 23 April 2009
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
  05.45.Df (Fractals)  
  05.65.+b (Self-organized systems)  
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https://cpl.iphy.ac.cn/10.1088/0256-307X/26/5/050502       OR      https://cpl.iphy.ac.cn/Y2009/V26/I5/050502
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HUANG Shou-Fang
ZHANG Ji-Qian
DING Shi-Jiang
[1] Wang Y Q, Wan Z D and Wang W 1998 J. Phys. Soc. Jpn. 67 3637
[2] Gong P L and Xu J X 2001 Phys. Rev. E 63 1906
[3] Gong P L, Xu J X and Hu S J 1999 Acta Biophys. Sin. 15 725
[4] Gong Y F, Ren W, Shi X Z and Xu J X 1999 Phys. Lett.A 258 253
[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] Wang M S, Hou Z H and Xin H W 2006 Chem. Phys.Chem. 7 579
[11] Meyer-Baese U 1998 Proc. SPIE 3390 560
[12] Reinker S, Li Y X and Kuske R 2006 Bull. Math.Biol. 68 1401
[13] Hindmarsh J L and Rose R M 1994 Biol. Sci. 346 129
[14] Wiesenfeld K and Moss F 1995 Nature 373 33
[15] Wu S G, Ren W, Kai F and Huang Z Q 2001 Phys. Lett.A 279 347
[16] Rose J E, Brugge J F, Arderson D J and Hind J E 1967 J. Neurophysiol. 30 769
[17] Siege R M 1990 Physica D 42 385
[18] Longtin A, Bulsara A and Moss F 1991 Phys. Rev.Lett. 67 656
[19] Longtin A 1993 J. Statist. Phys. 70 309
[20] Wu S G, He K F and Huang Z Q 2000 Phys. Rev. E 62 4417
[21] Hindmarsh J L and Rose R M 1982 Nature 296162
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