# Homogeneous Systems with a Quiescent Phase

Mathematical Modelling of Natural Phenomena (2008)

- Volume: 3, Issue: 7, page 115-125
- ISSN: 0973-5348

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topHadeler, K. P.. "Homogeneous Systems with a Quiescent Phase." Mathematical Modelling of Natural Phenomena 3.7 (2008): 115-125. <http://eudml.org/doc/222285>.

@article{Hadeler2008,

abstract = {
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.
},

author = {Hadeler, K. P.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {quiescence; homogeneous system; exponential solution; stability; non-linear eigenvalue
problem; predator-prey system; non-linear eigenvalue problem},

language = {eng},

month = {10},

number = {7},

pages = {115-125},

publisher = {EDP Sciences},

title = {Homogeneous Systems with a Quiescent Phase},

url = {http://eudml.org/doc/222285},

volume = {3},

year = {2008},

}

TY - JOUR

AU - Hadeler, K. P.

TI - Homogeneous Systems with a Quiescent Phase

JO - Mathematical Modelling of Natural Phenomena

DA - 2008/10//

PB - EDP Sciences

VL - 3

IS - 7

SP - 115

EP - 125

AB -
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.

LA - eng

KW - quiescence; homogeneous system; exponential solution; stability; non-linear eigenvalue
problem; predator-prey system; non-linear eigenvalue problem

UR - http://eudml.org/doc/222285

ER -

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