File:Exemple de noyau d'invariance.png

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Français : Le noyau d'invariance de l'ensemble de contraintes K rassemble les états à partir desquels toutes les trajectoires gouvernées par la dynamique restent dans K. La figure montre la trajectoire issue de A et la trajectoire issue de B (qui sort de K), B n'étant pas dans le noyau. La dynamique modélise l'eutrophisation d'un lac par une pseudo-sigmoïde avec les paramètres b=1,95 ; q=1,9 ; r=260/v ; m= 70/v avec v= 3,9 (volume du lac en milliards de m³)
English: The invariance kernel of K under dynamics S gathers the states of K from which all evolutions governed by S remain in K. Trajectory from state A stays in K. Trajectory from state B leaves K: it is not in the invariance kernel. The dynamics models lake eutrophication with a pseudo-sygmoid (b=1.95 ; q=1.9 ; r=260/v ; m= 70/v avec v= 3.9 (lake volume in billions of m³)
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Captions

Invariance kernel (in light bue) of dynamics <math>\frac {dP} {dt} =-bP(t) + L +r\frac {P(t)^{q}} {m^{q} + P(t)^{q}}</math> in constraint set <math>K=[Lmin,+\infty[ \times [0,Pmax]</math>.

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inception

22 January 2024

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current18:14, 22 January 2024Thumbnail for version as of 18:14, 22 January 2024759 × 792 (29 KB)IsadwikiUploaded own work with UploadWizard
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