Commit b4d50c2f authored by Ludovic Mailleret's avatar Ludovic Mailleret
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update AE notebook

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%% Cell type:markdown id: tags:
# Notebook d'aide et correction pour la séance EPU MAM4 Biomaths
*séance du 22/03/2021*
*séance du 21/03/2022*
*Ludovic Mailleret, Mars 2021*
*Ludovic Mailleret, Mars 2022*
## Populations isolées : le modèle de Malthus
Nous considérons le modèle de croissance de population suivant:
$$\dot x = (n-m) x$$
Vous trouverez dans ce qui suit le script complet de ce que nous avons vu, pas par pas, dans les sections précédentes.
### Définition des conditions initiales, des paramètres, du modèle et simulation de celui-ci
%% Cell type:code id: tags:
``` python
# on nettoie l'espace de travail
%reset -f
```
%% Cell type:code id: tags:
``` python
# import des modules numpy, matplotlib et de la fonction odeint depuis scipy
import numpy as np
import matplotlib.pyplot as plt
from scipy.integrate import odeint
```
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Nous définissons les conditions initiales et les paramètres et les encapsulons dans des `array`:
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``` python
# densité initiale de la population
x0 = 0.1
# encapsulation de la densité initiale
etat0_malthus = np.array([x0])
# paramètres du modèle
# taux de natalité
n = 3.0
# taux de mortalité
m = 2.0
# encapsulation des paramètres dans un array
params_malthus = np.array([n, m])
```
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Nous définissons ensuite les paramètres liés aux temps d'intégration `tspan` de l'équation différentielle:
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``` python
# temps d'intégration
# definition des paramètres du tspan
t_0 = 0.0 # temps initial
t_fin = 20.0 # temps final
pas_t = 0.01 # pas de temps de récupération des variables entre t_0 et t_fin
# définition du tspan
tspan = np.arange(t_0, t_fin, pas_t)
```
%% Cell type:markdown id: tags:
Nous définissons maintenant le modèle proprement dit, c'est à dire une fonction qui renvoit la valeur de la dérivée de(s) la(es) variable(s) d'état en fonction de la valeur de l'état, du temps et des paramètres :
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``` python
# définition du modèle de Malthus
def modele_malthus(etat, t, params):
x = etat # on recupere l'etat
n, m = params # on récupère les paramètres que l'on assigne à des paramètres locaux à la fonction
# on fera bien attention à l'ordre des paramètres défini plus haut dans l'encapsulation
xdot = (n-m)*x # on calcule la derivee de l'etat
return xdot # on renvoie la derivée calculée
```
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On passe à l'intégration proprement dite en utilisant la fonction `odeint()` :
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``` python
# intégration du modèle
int_malthus = odeint(modele_malthus, etat0_malthus, tspan, args=(params_malthus,), hmax=pas_t)
```
%% Cell type:markdown id: tags:
L'intégration est faite :
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``` python
int_malthus
```
%%%% Output: execute_result
array([[1.00000000e-01],
[1.01005023e-01],
[1.02020142e-01],
...,
[4.70826462e+07],
[4.75558347e+07],
[4.80337788e+07]])
%% Cell type:markdown id: tags:
Il reste maintenant à représenter cette simulation.
### Représentation graphique
Nous créons une figure et deux systèmes d'axes pour représenter deux sous-figures, puis nous traçons l'évolution de la variable en fonction du temps en échelle linéaire (gauche) ou semi-log (droite).
Vous pouvez découvrir différentes options des méthodes `subplots()`, `plot()`, `legend()`, l'utilisation de LaTeX dans les chaînes de caractères, ou une méthode utile de Python 3 pour compléter les chaines de caractères avec des valeurs via `.format()`
%% Cell type:code id: tags:
``` python
# création d'une figure, et de deux subplots (ax1, ax2)
fig1, (ax1, ax2) = plt.subplots(1, 2, figsize=(14, 8))
# premier subplot
# tracé des simulations par rapport au temps, échelle linéaire
ax1.plot(tspan, int_malthus, color='C0', label='population $x$')
ax1.legend(fontsize='14')
# labellisation des axes
ax1.set_xlabel('temps', fontsize='16')
ax1.set_ylabel('densité de population $x$', fontsize='16')
# titre de la figure
fig1.suptitle('Simulation du modèle de Malthus\n $n = {}, m = {}$'.format(n, m), va='top', fontsize='18')
# modification éventuelle des bornes des axes
ax1.set_ylim(bottom=None, top=None)
# ajout d'une grille
ax1.grid()
## second subplot
# tracé des simulations par rapport au temps, échelle logarithmique
ax2.plot(tspan, int_malthus, color='C0', label='population $x$')
ax2.legend(fontsize='14')
# echelle des ordonnees en log
ax2.set_yscale('log')
# labellisation des axes
ax2.set_xlabel('temps', fontsize='16')
# ajout d'une grille
ax2.grid()
```
%%%% Output: display_data
![](data:image/png;base64,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)
%% Cell type:markdown id: tags:
Le cas échéant on peut exporter la figure pour une ré-utilisation dans d'autres logiciels
%% Cell type:code id: tags:
``` python
# export
# permet d'enregistrer la figure fig1 au format png (sans trop d'espace autour)
fig1.savefig('Malthus.png', bbox_inches='tight')
```
%% Cell type:markdown id: tags:
La suite sur les prélèvements dans les modèles avec effets Allee par [ici](./biomaths_mam4_AE.ipynb)
......
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