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The phenomenon of stochastic resonance (SR) and coherence resonance (CR) in a bi-stable system driven by additive and multiplicative noises has been investigated. For the case that the system has uncorrelated or correlated additive and multiplicative noises, we introduce an appropriate index that can characterize both SR and CR at the same time. Applying the first-order Euler numerical computation to study the SR and CR, We can show that for small noise density, with the increase of additive noise density, and the appearance of CR, if we add a small periodic force to the bi-stable system, SR will occur almost at the same time. However, with increasing multiplicative noise density, the above conclusion may be satisfied only for correlated additive and multiplicative noises. Moreover, the effects of other parameters on CR and SR can be shown to be the same.
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Keywords:
- bi-stable system /
- stochastic resonance /
- coherence resonance
[1] Benzi R, Sutera A, Vulpiani A 1981 Phys. Rev. A 14 L453
[2] Nicolis C 1981 Solar Physics 74 473
[3] Anishchenko V S, Neiman A B, Moss F, Schimansky-Geier L 1999 Phys. Uspekhi 42 7
[4] Hu G, Ditzinger T, Ning C Z, Haken H 1993 Phys. Rev. Lett. 71 807
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[7] Zhou X R, Luo X S 2008 Acta Phys. Sin. 57 2849 (in Chinese) [周小荣, 罗晓曙 2008 57 2849]
[8] Cao Z J, Li P F, Hu G 2007 Chin. Phys. Lett. 24 882
[9] Dumas J, Marcus J 2012 Physica B 407 1750
[10] Fischer M, Stefani F, Gerbeth G 2008 Eur. Phys. J. B 65 547
[11] Jin Y F, Hu Y F 2007 Physica A 382 423
[12] Werner J P, Benner H, Florio B J, Stemle T 2011 Physica D 240 1863
[13] Pikovsky A S, Kurths J 1997 Phys. Rev. Lett. 78 775
[14] Badzey R L, Mohanty P 2005 Nature 437 995
[15] Doiron B, Lindner B, Longtin A, Maler L, Bastian J 2004 Phys. Rev. Lett. 93 048101
[16] Neiman A B, Russell D F 2004 Journal of Neurophysiology 92 492
[17] Zhang X Y, Xu W, Zhou B C 2011 Acta Phys. Sin. 6 60514 (in Chinese) [张晓燕, 徐伟, 周丙常 2012 60 60514]
[18] Zhang X Y, Xu W, Zhou B C 2012 Acta Phys. Sin. 61 030501(in Chinese) [张晓燕, 徐伟, 周丙常 2012 61 030501]
[19] Li J L, Zeng L Z 2011 Chin. Phys. B 20 010503
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[1] Benzi R, Sutera A, Vulpiani A 1981 Phys. Rev. A 14 L453
[2] Nicolis C 1981 Solar Physics 74 473
[3] Anishchenko V S, Neiman A B, Moss F, Schimansky-Geier L 1999 Phys. Uspekhi 42 7
[4] Hu G, Ditzinger T, Ning C Z, Haken H 1993 Phys. Rev. Lett. 71 807
[5] Chen J X 2006 Journal of Hulunbeir Collrge 14 85 (in Chinese) [陈进兴 2006 呼伦贝尔学院学报 14 85]
[6] Lindner B, Schimansky-Geier L 2000 Phys. Rev. E 61 6103
[7] Zhou X R, Luo X S 2008 Acta Phys. Sin. 57 2849 (in Chinese) [周小荣, 罗晓曙 2008 57 2849]
[8] Cao Z J, Li P F, Hu G 2007 Chin. Phys. Lett. 24 882
[9] Dumas J, Marcus J 2012 Physica B 407 1750
[10] Fischer M, Stefani F, Gerbeth G 2008 Eur. Phys. J. B 65 547
[11] Jin Y F, Hu Y F 2007 Physica A 382 423
[12] Werner J P, Benner H, Florio B J, Stemle T 2011 Physica D 240 1863
[13] Pikovsky A S, Kurths J 1997 Phys. Rev. Lett. 78 775
[14] Badzey R L, Mohanty P 2005 Nature 437 995
[15] Doiron B, Lindner B, Longtin A, Maler L, Bastian J 2004 Phys. Rev. Lett. 93 048101
[16] Neiman A B, Russell D F 2004 Journal of Neurophysiology 92 492
[17] Zhang X Y, Xu W, Zhou B C 2011 Acta Phys. Sin. 6 60514 (in Chinese) [张晓燕, 徐伟, 周丙常 2012 60 60514]
[18] Zhang X Y, Xu W, Zhou B C 2012 Acta Phys. Sin. 61 030501(in Chinese) [张晓燕, 徐伟, 周丙常 2012 61 030501]
[19] Li J L, Zeng L Z 2011 Chin. Phys. B 20 010503
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