The onset and extinction of neural spiking: A numerical bifurcation approach

Journal of Computational Neuroscience

Volumn 18, Issue 3, 2005, Pages 265-274

  Govaerts, Willy ^a   Sautois, Bart ^a  

^a GHENT UNIVERSITY   (Belgium)

Author keywords

Classification; Morris Lecar; Neural models; Spiking

Indexed keywords

APPLIED CURRENT; BIFURCATION DIAGRAM; EQUILIBRIUM CYCLE; LIMIT CYCLE BIFURCATION; MORRIS-LECAR; MORRIS-LECAR MODEL; NEURAL MODELLING; PARAMETER RANGE; SPIKING; TWO PARAMETER;

BIFURCATION (MATHEMATICS);

AMPLITUDE MODULATION; ANALYTICAL PARAMETERS; ARTICLE; CLASSIFICATION; COMPUTER PROGRAM; CONTROLLED STUDY; FREQUENCY ANALYSIS; LATENT PERIOD; MATHEMATICAL COMPUTING; MATHEMATICAL MODEL; NERVE CELL MEMBRANE STEADY POTENTIAL; OSCILLATION; PRIORITY JOURNAL; QUALITATIVE ANALYSIS; SPIKE WAVE;

EID: 18144400379     PISSN: 09295313     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10827-005-0328-9     Document Type: Article

References (20)

1. Bazykin AD (1985) Mathematical Biophysics of Interacting Populations. Nauka, Moscow (in Russian).
2. AD Bazykin 1998 Nonlinear Dynamics of Interacting Populations World Scientific Singapore
3. Crook SM, Ermentrout GB, Bower JM (1998) Spike frequency adaptation affects the synchronization properties of networks of cortical oscillators. Neural Comput. 10: 837-854.
4. Dhooge A, Govaerts W, Kuznetsov Yu A (2003) MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs. ACM TOMS 29(2): 141-164.
5. Dhooge A, Govaerts W, Kuznetsov Yu A, Mestrom W, Riet AM (2003) A Continuation Toolbox in matlab. Manual, http://allserv.UGent.be/~ajdhooge/doc_cl_matcont.zip.
6. Doedel EJ, Champneys AR, Fairgrieve TF, Kuznetsov Yu A, Sandstede B, Wang XJ (1997-2000) AUTO97-AUTO2000: Continuation and Bifurcation Software for Ordinary Di.erential Equations (with HomCont). User's Guide, (Concordia University, Montreal, Canada) http://sourceforge.net/projects/auto2000
7. Ermentrout GB (1996) Type I membranes, phase resetting curves and synchrony. Neural Comput. 8(5): 979-1001.
8. Ermentrout GB, Pascal M, Gutkin B (2001) The Effects of Spike Frequency Adaptation and Negative Feedback on the Synchronization of Neural Oscillators. Neural Comput. 13(6): 1285-1310.
9. Fall CP Marland ES Wagner JM Tyson JJ 2002 Computational Cell Biology Springer-Verlag New York, NY
10. Govaerts W, Sautois B (2005) Bifurcation software in Matlab with applications in neuronal modeling. Comput. Meth. Prog. Bio. 77(2): 141-153.
11. Hodgkin AL (1948) The local electric changes associated with repetitive action in a non-medullated axon. J. Physiol. 107: 165-181.
12. Hos C, Champneys A, Kullmann L (2003) Bifurcation analysis of surge and rotating stall in the Moore-Greitzer compression system. IMA J. App. Math. 68: 205-228.
13. Izhikevich EM (2000) Neural excitability, spiking and bursting. Int. J. Bifurcat. Chaos 10(6): 1171-1266.
14. Khibnik A, Krauskopf B, Rousseau C (1998) Global study of a family of cubic Lie'nard equations. Nonlinearity 11: 1505-1519.
15. Kuznetsov Yu A 1998 Elements of Applied Bifurcation Theory Springer-Verlag New York, NY
16. Kuznetsov Yu, A Levitin VV (1997) content: Integrated Environment for Analysis of Dynamical Systems. www.math.uu.nl/people/kuznet/CONTENT (CWI, Amsterdam).
17. Morris C, Lecar H (1981) Voltage oscillations in the barnacle giant muscle fiber. Biophys. J. 35: 193-213.
18. Rinzel J Ermentrout B 1989 Analysis of Neural Excitability and Oscillations In: Koch C Segev I eds. Methods in Neuronal Modeling: From Synapses to Networks MIT Press Cambridge, MA 135-169
19. Tsumoto K, Yoshinaga T, Aihara K, Kawakami H (2002) Bifurcations in Morris-Lecar neuron model. Proceedings of the Int. Symp. on Nonlinear Theory and its Appls., Xi'an, China, pp. 363-366.
20. van Vreeswijk C, Hansel, D (2001) Patterns of synchrony in neural networks with spike adaptation. Neural Comput. 13: 959-992.