| GENERAL |
|
|
|
|
Bursting Behavior in the Piece-Wise Linear Planar Neuron Model with Periodic Stimulation |
| JI Ying, WANG Ya-Wei** |
Faculty of Science, Jiangsu University, Zhenjiang 212013
|
|
| Cite this article: |
|
JI Ying, WANG Ya-Wei 2015 Chin. Phys. Lett. 32 040201 |
|
|
|
|
Abstract A piece-wise linear planar neuron model with periodic stimulation which can mimic the behavior of bursting is explored. The periodic bursting with three frequencies can be observed in numerical simulation. We present an analysis of bursting in this non-smooth non-autonomous system by considering the system as a generalized autonomous system and introduce an appropriate form of the associated generalized equilibrium solution. The bifurcation mechanism of bursting as well as the coexistence of three frequencies is investigated in detail.
|
|
|
Received: 12 December 2014
Published: 30 April 2015
|
|
| PACS: |
02.30.Oz
|
(Bifurcation theory)
|
| |
02.60.Cb
|
(Numerical simulation; solution of equations)
|
| |
05.45.Pq
|
(Numerical simulations of chaotic systems)
|
|
|
|
|
|
[1] Johnson S W, Seutin V and North R A 1992 Science 258 665
[2] Ivanchenko M V, Osipov G V, Shalfeev V D and Kurths J 2007 Phys. Rev. Lett. 98 108101
[3] Ji Y and Bi Q S 2011 Chin. Phys. Lett. 28 090201
[4] Wang H X, Wang Q Y and Zheng Y H 2014 Sci. Chin. Technol. Sci. 57 872
[5] Gu H G and Chen S G 2014 Sci. Chin. Technol. Sci. 57 864
[6] Hodgkin A L and Huxley A F 1952 J. Physiol. 117 500
[7] Chay T R, Fan Y S and Lee Y S 1995 Int. J. Bifurcation Chaos Appl. Sci. Eng. 5 595
[8] Rinzel J 1985 Ordinary Partial Differential Equations (Berlin: Springer-Verlag)
[9] Sherman A and Rinzel J 1992 Proc. Natl. Acad. Sci. USA 89 2471
[10] Tiesinga P H E 2002 Phys. Rev. E 65 041913
[11] Coombes S 2008 SIAM J. Appl. Dyn. Syst. 7 1101
[12] Fitzhugh R 1961 Biophys. J. 1 445
[13] Yamashita Y and Torikai H 2014 IEEE T. Circuits-II: Express Briefs 61 54
[14] Izhikevich E M 2000 Int. J. Bifurcation Chaos Appl. Sci. Eng. 10 1171
[15] Yang Z Q and Lu Q S 2008 Sci. Chin. Phys. Mech. Astron. 51 687
[16] Zhang F, Lubbe A, Lu Q S and Su J Z 2014 Discrete Continuous Dynamical Syst. Ser. S 7 1363
[17] Xie Y, Kang Y M, Liu Y and Wu Y 2014 Sci. Chin. Technol. Sci. 57 914
[18] Tonnelier A 2003 SIAM J. Appl. Math. 63 459
[19] Jaume L, Manuel O, Manuel O and Enrique P 2013 Nonlinear Anal.: Real World Appl. 14 2002
[20] Leine R I 2006 Physica D 223 121 |
|
Viewed |
|
|
|
Full text
|
|
|
|
|
Abstract
|
|
|
|
|
