The FitzHugh-Nagumo Model: Bifurcation and Dynamics

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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 emphasized. 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 analyzed. New types of codimension-one and -two bifurcations of planar systems were found. A detailed global bifurcation diagram concludes the work. This volume should be useful 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.