Geodesic
On nonlinear singularly perturbed problems in biology
Matematičeskoe modelirovanie, Tome 22 (2010) no. 9, pp. 107-115

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Two nonlinear singularly perturbed model problems on heartbeat and nerve impulse are discussed with sufficient theoretical material. Data analysis of non-autonomous models is made, and is built models' phase portrait. We also give oscillation graphs of heartbeat mathematical model (cardiogram analog) and graphs of nerve impulse transmission with considering condition of Hopf bifurcation appearance. The frontier layer presence is marked at each graph in a $t=0$ neighborhood.
Keywords: models of the heartbeat and nerve impulse, singularly perturbed problems, stability. 
@article{MM_2010_22_9_a7,
     author = {Yu. A. Konyaev and V. I. Bezyaev and O. N. Filippova},
     title = {On nonlinear singularly perturbed problems in biology},
     journal = {Matemati\v{c}eskoe modelirovanie},
     pages = {107--115},
     publisher = {mathdoc},
     volume = {22},
     number = {9},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MM_2010_22_9_a7/}
}
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Yu. A. Konyaev; V. I. Bezyaev; O. N. Filippova. On nonlinear singularly perturbed problems in biology. Matematičeskoe modelirovanie, Tome 22 (2010) no. 9, pp. 107-115. http://geodesic.mathdoc.fr/item/MM_2010_22_9_a7/