, du temps t, noté i(t) = i k , pour un autre état en particulier au temps t + ?t, noté i(t + ?t) = i l , avec i k ? i l , peut être approximée par : P[i(t + ?t) = i l ? i k | i(t) = i k , x(t), y(t), e(t, ?t ? p(i k ? i l | x(t), y(t), e(t), t) [IV.3.7]
, exprimer l'état complet du système au temps t par (i(t), x(t), y(t), e(t)) = (i k , x k ± ? x , y k ± ? y , e k ± ? e ), fournissent des approximations numériques
, x(t + ?t), y(t + ?t), e(t + ?t)) = (i k , x k ± ? x , y(t) ± ? y , e(t) ± ? e ) | (i(t), x(t), y(t), e(t)) = (i l
, x , y k ± ? y , e k ± ? e ), sachant qu'il est dans un état particulier au temps t, noté (i(t), x(t), y(t), e(t)) = (i l , x l , y l , e l ), peut alors être approximée par, e(t + ?t)) = (i k , x k ± ? x , y(t) ± ? y , e(t) ± ? e ) | (i(t), x(t), y(t), e(t)) = (i l , x l , y l
, (t) + E M (? M ? dt, ? M ) ? I 1 (? M (t) < C M ) ? I 1 (SPM(t) = 3) [IV.3.31] avec SPM(t), la variable d'état de la pompe
, de forme ? M ? dt = 0.5 ? dt et de paramètre d'échelle 1/? M = 400 donné dans le Tableau IV.3.4. D'après l'Équation IV.3.16, le couple total de la pompe est donc égal à C M ? ? M (t) lorsque SPM(t) = 3. Comme l'incrément des déviations du couple de la pompe dans l'intervalle de temps [t ; t + dt], défini par E M (? M ? dt, ? M ) ? I 1 (? M (t) < C M ) ? I 1 (SPM(t) = 3), est indépendant du temps t (mais, évidement, fonction de dt, une variable aléatoire distribuée selon une loi Gamma de paramètre ce processus stochastique est stationnaire, étant donné I 1 (? M (t) < C M ) ? I 1 (SPM(t) = 3). (Pour les analyses numériques en utilisant le formalisme présenté dans la Section IV.3.2.1 : dt = ?t
, ) ; T i (t), la variable du processus qui est la température du sodium dans le canal i, définie dans la Section IV
, 1, et le réseau de Petri correspondant décrit sur la Figure IV.3.6. En accord avec ce formalisme, chaque variable a été modélisée séparément (excepté pour les concentrations des précurseurs C i (t), avec i = 1, 2, 3, 4, 5, 6, qui ont été modélisées par un vecteur, noté C(t)). Les variables du processus sont décrites sur la partie gauche de la Figure IV.3.6, et peuvent être distinguées par des places grises, de traits continus, et qui sont associées à des méta-transitions (cf. légende de la Figure IV.3.1). La métatransition associée à la variable du flux de sodium (G(t)) a été explicitement représentée parce que la dérivée incluse dans cette méta-transition, Le système a été modélisé en utilisant le formalisme présenté dans la Section IV.3.2
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