Geodesic
Homogeneous Systems with a Quiescent Phase
K. P. Hadeler1
1 Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, USA
Mathematical modelling of natural phenomena, Tome 3 (2008) no. 7, pp. 115-125

Voir la notice de l'article provenant de la source EDP Sciences

Recently the effect of a quiescent phase (or dormant/resting phase in applications) on the dynamics of a system of differential equations has been investigated, in particular with respect to stability properties of stationary points. It has been shown that there is a general phenomenon of stabilization against oscillations which can be cast in rigorous form. Here we investigate, for homogeneous systems, the effect of a quiescent phase, and more generally, a phase with slower dynamics. We show that each exponential solution of the original system produces two exponential solutions of the extended system whereby the stability properties can be controlled.
DOI : 10.1051/mmnp:2008044

K. P. Hadeler 1

1 Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, USA 
@article{10_1051_mmnp:2008044,
     author = {K. P. Hadeler},
     title = {Homogeneous {Systems} with a {Quiescent} {Phase}},
     journal = {Mathematical modelling of natural phenomena},
     pages = {115--125},
     publisher = {mathdoc},
     volume = {3},
     number = {7},
     year = {2008},
     doi = {10.1051/mmnp:2008044},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2008044/}
}
TY  - JOUR
AU  - K. P. Hadeler
TI  - Homogeneous Systems with a Quiescent Phase
JO  - Mathematical modelling of natural phenomena
PY  - 2008
SP  - 115
EP  - 125
VL  - 3
IS  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2008044/
DO  - 10.1051/mmnp:2008044
LA  - en
ID  - 10_1051_mmnp:2008044
ER  - 
%0 Journal Article
%A K. P. Hadeler
%T Homogeneous Systems with a Quiescent Phase
%J Mathematical modelling of natural phenomena
%D 2008
%P 115-125
%V 3
%N 7
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.1051/mmnp:2008044/
%R 10.1051/mmnp:2008044
%G en
%F 10_1051_mmnp:2008044
K. P. Hadeler. Homogeneous Systems with a Quiescent Phase. Mathematical modelling of natural phenomena, Tome 3 (2008) no. 7, pp. 115-125. doi: 10.1051/mmnp:2008044

Cité par Sources :