Homogeneous Systems with a Quiescent Phase

K. P. Hadeler

Mathematical Modelling of Natural Phenomena (2008)

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

Abstract

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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.

How to cite

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Hadeler, 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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