Chin. Phys. Lett.  2013, Vol. 30 Issue (1): 010503    DOI: 10.1088/0256-307X/30/1/010503
GENERAL |
Single-Hopf Bursting in Periodic Perturbed Belousov–Zhabotinsky Reaction with Two Time Scales
LI Xiang-Hong1,2, BI Qin-Sheng2**
1Department of Mathematics and Physics, Shijiazhuang Tiedao University, Shijiazhuang 050043
2Faculty of Civil Engineering and Mechanics, Jiangsu University, Zhenjiang 212013
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LI Xiang-Hong, BI Qin-Sheng 2013 Chin. Phys. Lett. 30 010503
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Abstract By introducing weak periodic perturbation to the Oregonator, we investigate a mathematical model with two time scales. The novel dynamical phenomena called the single-Hopf bursting with unusually quiescent state are observed. The related bifurcation mechanism is presented by means of the transition portrait and slow-fast analysis, which has rarely been reported in the previous works associated with the Oregonator model. Furthermore, the influence of forcing amplitude on bursting behaviors is studied. Further investigation finds that excitation amplitude may play an important role in a two-timescale system with the slow procedure dominated by periodic perturbation.
Received: 02 November 2012      Published: 04 March 2013
PACS:  05.45.-a (Nonlinear dynamics and chaos)  
  82.40.Bj (Oscillations, chaos, and bifurcations)  
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https://cpl.iphy.ac.cn/10.1088/0256-307X/30/1/010503       OR      https://cpl.iphy.ac.cn/Y2013/V30/I1/010503
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Articles by authors
LI Xiang-Hong
BI Qin-Sheng
[1] Lu Q S, Yang Z Q, Duan L X, Gu H G and Ren W 2009 Chaos Solitons Fractals 40 577
[2] Bi Q S 2010 Sci. Chin. Technol. Sci. 53 748
[3] Savino G V and Formigli C M 2009 Biosystems 97 9
[4] Vidal A 2006 Positive Syst. LNCIS 341 439
[5] Butera R J Jr, Rinzel J and Smith J C 1999 J. Neurophysiol. 82 382
[6] Zhou G H, Xu J P, Bao B C, Zhang F and Liu X S 2010 Chin. Phys. Lett. 27 090504
[7] Song M, Wang B N and Xu G S 2003 Chin. Phys. B 12 189
[8] Davis M J and Klippenstein S J 2002 J. Phys. Chem. A 106 5860
[9] Mease K D 2005 Appl. Math. Comput. 164 627
[10] Han X J and Bi Q S 2009 Acta Phys. Sin. 373 3643 (in Chinese)
[11] Li X H and Bi Q S 2012 Chin. Phys. B 21 060505
[12] Curtu R 2010 Physica D 239 504
[13] Holden L and Erneux T 1993 SIAM J. Appl. Math. 53 1045
[14] Organ L, Kiss I Z and Hudson J L 2003 J. Phys. Chem. B 107 6648
[15] Li X H and Bi Q S 2012 Acta Phys. Sin. 2 020504 (in Chinese)
[16] Agladze K, Obata S and Yoshikawa K 1995 Physica D 84 238
[17] Hitoshi M, Tomohiko Y and Yoshitomi M 2005 Physica D 205 275
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