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

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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 
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
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