En esta sección, consideramos la distribución de una población de diferentes edades. Dejar\(x(t)\) ser un vector de 100 con\(x_i(t)\) denotar el número de personas con agente\(i−1\).
Entonces podemos modelar la población con los sistemas dinámicos. Consideramos primero a los 0 años de edad. Incluye a todos los recién nacidos de todas las edades, así que tenemos\(x_1(t+1) = b^{\top}x(t)\). Entonces consideramos todas las demás edades para\(i > 1\). \(x_i(t+1) = (1-d_i)x_{i-1}(t)\)
population = np.array([
3.94415, 3.97807, 4.09693, 4.11904, 4.06317, 4.05686, 4.06638, 4.03058,
4.04649, 4.14835, 4.17254, 4.11442, 4.10624, 4.11801, 4.16598, 4.24282,
4.31614, 4.39529, 4.50085, 4.58523, 4.51913, 4.35429, 4.26464, 4.19857,
4.24936, 4.26235, 4.15231, 4.24887, 4.21525, 4.22308, 4.28567, 3.97022,
3.98685, 3.88015, 3.83922, 3.95643, 3.80209, 3.93445, 4.12188, 4.36480,
4.38327, 4.11498, 4.07610, 4.10511, 4.21150, 4.50887, 4.51976, 4.53526,
4.53880, 4.60590, 4.66029, 4.46463, 4.50085, 4.38035, 4.29200, 4.25471,
4.03751, 3.93639, 3.79493, 3.64127, 3.62113, 3.49260, 3.56318, 3.48388,
2.65713, 2.68076, 2.63914, 2.64936, 2.32367, 2.14232, 2.04312, 1.94932,
1.86427, 1.73696, 1.68449, 1.62008, 1.47107, 1.45533, 1.40012, 1.37119,
1.30851, 1.21287, 1.16142, 1.07481, 0.98572, 0.91472, 0.81421, 0.71291,
0.64062, 0.53800, 0.43556, 0.34499, 0.28139, 0.21698, 0.16944, 0.12972,
0.09522, 0.06814, 0.04590, 0.03227])
d = np.array([
0.00623, 0.00044, 0.00027, 0.00020, 0.00016, 0.00012, 0.00011, 0.00011,
0.00012, 0.00011, 0.00010, 0.00013, 0.00013, 0.00015, 0.00020, 0.00025,
0.00037, 0.00047, 0.00064, 0.00071, 0.00076, 0.00087, 0.00087, 0.00088,
0.00094, 0.00092, 0.00095, 0.00093, 0.00099, 0.00101, 0.00103, 0.00109,
0.00110, 0.00114, 0.00115, 0.00120, 0.00131, 0.00137, 0.00146, 0.00156,
0.00162, 0.00185, 0.00201, 0.00216, 0.00243, 0.00258, 0.00298, 0.00325,
0.00351, 0.00387, 0.00413, 0.00454, 0.00494, 0.00533, 0.00571, 0.00602,
0.00670, 0.00710, 0.00769, 0.00828, 0.00860, 0.00932, 0.00998, 0.01101,
0.01250, 0.01282, 0.01404, 0.01515, 0.01687, 0.01830, 0.01967, 0.02133,
0.02347, 0.02562, 0.02800, 0.03083, 0.03441, 0.03711, 0.04126, 0.04448,
0.04964, 0.05539, 0.06149, 0.06803, 0.07673, 0.08561, 0.09540, 0.10636,
0.11802, 0.13385, 0.15250, 0.16491, 0.18738, 0.20757, 0.22688, 0.25196,
0.27422, 0.29239, 0.32560, 0.34157])
b = np.array([
0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000,
0.00000, 0.00000, 0.00020, 0.00020, 0.00020, 0.00020, 0.00020, 0.01710,
0.01710, 0.01710, 0.01710, 0.01710, 0.04500, 0.04500, 0.04500, 0.04500,
0.04500, 0.05415, 0.05415, 0.05415, 0.05415, 0.05415, 0.04825, 0.04825,
0.04825, 0.04825, 0.04825, 0.02250, 0.02250, 0.02250, 0.02250, 0.02250,
0.00510, 0.00510, 0.00510, 0.00510, 0.00510, 0.00035, 0.00035, 0.00035,
0.00035, 0.00035, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000,
0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000,
0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000,
0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000,
0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000,
0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000, 0.00000,
0.00000, 0.00000, 0.00000, 0.00000])
plt.subplot(1,3,1)
plt.plot(population)
plt.title('population in 2010')
plt.subplot(1,3,2)
plt.plot(b)
plt.title('birth rate in 2010')
plt.subplot(1,3,3)
plt.plot(d)
plt.title('death rate in 2010')
plt.show()