The FitzHugh-Nagumo Model
Subtitle: Bifurcation and Dynamics
By: by C. Rocşoreanu, A. Georgescu, N. Giurgiţeanu
Contributors: Georgescu, A.; Giurgiţeanu, N.
Series: Mathematical Modelling: Theory and Applications -- 10; Mathematical Modelling: Theory and Applications -- 10
Publisher: Springer Netherlands
Published: 2000
Place of publication: Dordrecht
Language: eng
Format: [electronic resource] :
Number of pages: 237
ISBN-13: 9789048155125; 9789401595483
Subjects: Biochemistry; Mathematics; Differential Equations; Cardiology
Description: This application-oriented monograph presents a comprehensive theoretical and numerical investigation of all types of oscillators and bifurcations (such as Hopf, Bogdanov-Takens, Bautin, and homoclinic) generated by the FitzHugh-Nagumo model. The wide diversity of the oscillators as used in electrophysiology, biology, and engineering is emphasised. Various asymptotic behaviours are revealed. The dramatic changes in oscillations connected with the emergence or disappearance of concave limit cycles are investigated. Codimension of bifurcations is minutely analysed. New types of codimension one and two bifurcations of planar systems were found. A detailed global bifurcation diagram concludes the work. Audience: This volume will be of interest to researchers and graduate students whose work involves the mathematics of biology, ordinary differential equations, approximations and expansions, cardiac electrophysiology, biological transport, and cell membranes.
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