Bifurcation and singularities in models of biosystems
Faina Berezovskaya
Mathematical Department, Howard University
2400 Sixth Street, NW,Washington, DC 20059 USA
fsberezo@hotmail.com
One of the most important aspects of the application of mathematical modeling
is the study of the system behavior near the "dangerous boundaries" of the
values of parameters and variables arising in regards to reorganizations (possibly
catastrophic) in the system behavior. The qualitative behavior of complex (bio)system
near critical modes may be described usually by a «low-dimensional» nonlinear
model depending on some parameters whose analysis includes the construction of a
"structural portrait", that is the splitting of parameter space into areas with
different modes of model functioning, Bifurcation approach allows to define
domains of parameter space where population persistence is possible and show the
boundaries whose intersecting leads to population extinction.
From other side, an existence in a model phase/parameter degenerations and/or
singularities can be a ‘sign’ of the existence of critical modes in the
modelling system.
Discussions of mentioned problems and consideration of corresponding models are
main topics of the section.