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Transitions of different neuronal firing patterns in the Chay model are explored by numerical simulation of three firing sequences observed in experiments on neural pacemakers, and the bifurcation analysis of limit cycle. Firstly,the transitions of periodic firing patterns through a pair of period-doubling bifurcations are obtained. Secondly,a supercritical and a subcritical period-doubling bursting sequences with different appearances lead to chaos,and then transit to an inverse period-doubling spiking sequence in different ways,separately. Finally,we reveal the true nature of period-adding bursting sequence without chaotic bursting,which is closely related to period-doubling bifurcation.
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Keywords:
- transitions of firing patterns /
- period-doubling bifurcation /
- period-adding bursting sequence
[1] Guevara M R,Glass L,Shrier A 1981 Science 214 1350
[2] Matsumoto G,Takahashi N,Hanyu Y 1987 Chaos,phase locking and normal squid axons. In Chaos in biological systems (New York:Plenum)
[3] Hayashi H,Ishizuka S 1987 Chaos in molluscan neuron In Chaos in biological systems (New York:Plenum)
[4] Steriade M,Jones E G,Llinas R R 1990 Thalamic Oscillations and Signaling (New York:Jphn Wiley)
[5] Schafer K,Braun H A,Rempe L 1988 Prog. Brain Res. 74 29
[6] Li L,Gu H G,Yang M H,Liu Z Q,Ren W 2004 Int. J. Bif. and Chaos 14 1813
[7] Mosekide E,Lading B,Yanchuk S,Maistrenko Y. 2001 BioSystems 63 3
[8] Doi S,Nabetani S,Kumagai S 2001 Biol. Cybern. 85 51
[9] Gao Z Y,Lu Q S 2007 Chin. Phys. 16 2479
[10] Yang Z Q,Lu Q S 2006 Chin. Phys. 15 518
[11] Holden A V,Fan Y S 1992 Chaos,Solitons and Fractals 2 221
[12] Holden A V,Fan Y S 1992 Chaos,Solitons and Fractals 2 349
[13] Holden A V,Fan Y S 1992 Chaos,Solitons and Fractals 2 583
[14] Xie Y,Xu J X,Kang Y M,Hu S J,Duan Y B 2003 Acta Phys. Sin. 52 1112 (in Chinese) [谢 勇、徐健学、康艳梅、胡三觉、段玉斌 2003 52 1112]
[15] Chay T R,Fan Y S,Lee Y S 1995 Int. J. Bif. and Chaos 5 595
[16] Chay T R 1985 Physica D 16 233
[17] Wu Y,Xu J X,He D H,Jin W Y 2005 Acta Phys. Sin. 54 3457 (in Chinese) [吴 莹、徐健学、何岱海、靳伍银 2005 54 3457]
[18] Wang B Y,Xu W,Xing Z C 2009 Acta Phys. Sin. 90 5865 (in Chinese) [王宝燕、徐 伟、邢真慈 2009 90 5865]
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[1] Guevara M R,Glass L,Shrier A 1981 Science 214 1350
[2] Matsumoto G,Takahashi N,Hanyu Y 1987 Chaos,phase locking and normal squid axons. In Chaos in biological systems (New York:Plenum)
[3] Hayashi H,Ishizuka S 1987 Chaos in molluscan neuron In Chaos in biological systems (New York:Plenum)
[4] Steriade M,Jones E G,Llinas R R 1990 Thalamic Oscillations and Signaling (New York:Jphn Wiley)
[5] Schafer K,Braun H A,Rempe L 1988 Prog. Brain Res. 74 29
[6] Li L,Gu H G,Yang M H,Liu Z Q,Ren W 2004 Int. J. Bif. and Chaos 14 1813
[7] Mosekide E,Lading B,Yanchuk S,Maistrenko Y. 2001 BioSystems 63 3
[8] Doi S,Nabetani S,Kumagai S 2001 Biol. Cybern. 85 51
[9] Gao Z Y,Lu Q S 2007 Chin. Phys. 16 2479
[10] Yang Z Q,Lu Q S 2006 Chin. Phys. 15 518
[11] Holden A V,Fan Y S 1992 Chaos,Solitons and Fractals 2 221
[12] Holden A V,Fan Y S 1992 Chaos,Solitons and Fractals 2 349
[13] Holden A V,Fan Y S 1992 Chaos,Solitons and Fractals 2 583
[14] Xie Y,Xu J X,Kang Y M,Hu S J,Duan Y B 2003 Acta Phys. Sin. 52 1112 (in Chinese) [谢 勇、徐健学、康艳梅、胡三觉、段玉斌 2003 52 1112]
[15] Chay T R,Fan Y S,Lee Y S 1995 Int. J. Bif. and Chaos 5 595
[16] Chay T R 1985 Physica D 16 233
[17] Wu Y,Xu J X,He D H,Jin W Y 2005 Acta Phys. Sin. 54 3457 (in Chinese) [吴 莹、徐健学、何岱海、靳伍银 2005 54 3457]
[18] Wang B Y,Xu W,Xing Z C 2009 Acta Phys. Sin. 90 5865 (in Chinese) [王宝燕、徐 伟、邢真慈 2009 90 5865]
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