An organizing center for planar neural excitability

Neurocomputing

Volumn 32-33, Issue , 2000, Pages 757-765

  Gall, Walter G ^a   Zhou, Ying ^a  

^a RHODE ISLAND COLLEGE   (United States)

Author keywords

Bifurcation; Canonical model; Hodgkin Huxley; Morris Lecar; Normal form

Indexed keywords

BIFURCATION (MATHEMATICS); COMPUTATIONAL METHODS; DIFFERENTIAL EQUATIONS; MATHEMATICAL TRANSFORMATIONS; MEMBRANES; PROBLEM SOLVING;

BOGDANOV-TAKENS POINTS; CANONICAL MODEL; MORRIS-LECAR AND HODGKIN-HUXLEY MODEL; NORMAL FORM; SECOND ORDER CUBIC DYNAMICAL SYSTEM;

NEURAL NETWORKS;

ARTICLE; HODGKIN HUXLEY EQUATION; MATHEMATICAL ANALYSIS; MATHEMATICAL MODEL; MEMBRANE MODEL; MEMBRANE POTENTIAL; NERVE CELL EXCITABILITY; PARAMETER; PRIORITY JOURNAL;

EID: 18344405260     PISSN: 09252312     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0925-2312(00)00241-1     Document Type: Article

References (12)

1. Borisyuk R., Kirillov A.B. Bifurcation analysis of a neural network model. Biol. Cybernet. 66:1992;319-325.
2. Dumortier F., Roussarie R., Sotomayor J., Zoladek H. Bifurcations of Planar Vector Fields: Nilpotent Singularities and Abelian Integrals, Lecture Notes in Mathematics, Vol. 1480. 1991;Springer, Berlin.
3. Ermentrout B. Type I membranes, phase resetting curves, and synchrony. Neural Comput. 8:1996;979-1001.
4. Gall W.G., Zhou Y. Including a second inward conductance in Morris and Lecar dynamics. Neurocomputing. 26:1999;131-136.
5. Guckenheimer J. Multiple bifurcation problems for chemical reactors. Physica D. 20:1986;1-20.
6. Guckenheimer J., Labouriau I.S. Bifurcations of the Hodgkin and Huxley equations: a new twist. Bull. Math. Biol. 55:1993;937-952.
7. Holden A.V., Muhamad M.A., Schierwagen A.K. Repolarizing currents and periodic activity in nerve membrane. J. Theoret. Neurobiol. 4:1985;61-71.
8. Hoppensteadt F.C., Izhikevich E.I. Weakly Connected Neural Networks, Applied Mathematical Sciences, Vol. 126. 1997;Springer, New York.
9. H.W. Hui, W.G. Gall, Parameter study of nerve and muscle fibers, Scientific Computation Project Report and Path Continuation Software Tools, Department of Mathematics, University of Science and Technology, Hong Kong, 1996.
10. Kuznetsov Y.A. Elements of Applied Bifurcation Theory, Applied Mathematical Sciences, Vol. 112. 1995;Springer, Berlin.
11. Rinzel J., Ermentrout B. Analysis of neural excitability and oscillations. Koch C., Segev I. Methods in Neuronal Modeling, 2nd Edition. 1998;251-291 MIT, Cambridge MA.
12. Schecter S. The saddle-node separatrix-loop bifurcation. SIAM J. Math. Anal. 18:1987;1142-1156.