Computation of equilibrium states and bifurcations using interval analysis: Application to food chain models

Food chains and webs in the environment are highly nonlinear and interdependent systems. When these systems are modeled using simple sets of ordinary differential equations, these models can exhibit very rich and complex mathematical behaviors. We present here a new equation-solving technique for co...

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Vydáno v:Ecological modelling Ročník 203; číslo 3; s. 495 - 510
Hlavní autoři: Gwaltney, C. Ryan, Luo, WenTao, Stadtherr, Mark A.
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 10.05.2007
Elsevier
Témata:
Animal, plant and microbial ecology
Bifurcations
Biological and medical sciences
Computational method
Equilibrium states
Food chain
Fundamental and applied biological sciences. Psychology
General aspects. Techniques
Interval analysis
Methods and techniques (sampling, tagging, trapping, modelling...)
Computational method
Interval analysis
Bifurcations
Food chain
Equilibrium states
Trophic chain
Equilibrium state
Models
Analysis method
Equilibrium states Bifurcations Food chain Computational method Interval analysis
Interval
ISSN:0304-3800, 1872-7026
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Shrnutí:Food chains and webs in the environment are highly nonlinear and interdependent systems. When these systems are modeled using simple sets of ordinary differential equations, these models can exhibit very rich and complex mathematical behaviors. We present here a new equation-solving technique for computing all equilibrium states and bifurcations of equilibria in food chain models. The method used is based on interval analysis, in particular an interval-Newton/generalized-bisection algorithm. Unlike the continuation methods often used in this context, the interval method provides a mathematical and computational guarantee that all roots of a nonlinear equation system are located. The technique is demonstrated using three different food chain models, and results of the computations are used to compare the models.
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ISSN:0304-3800
1872-7026
DOI:10.1016/j.ecolmodel.2006.12.015