mhjensen
44 lines
1.3 KiB
Python
44 lines
1.3 KiB
Python
import numpy as np
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import matplotlib.pyplot as plt
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def solver(m, H0, L0, dt, a, b, c, d, t0):
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"""Solve the difference equations for H and L over m years
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with time step dt (measured in years."""
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num_intervals = int(m/float(dt))
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t = np.linspace(t0, t0 + m, num_intervals+1)
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H = np.zeros(t.size)
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L = np.zeros(t.size)
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print 'Init:', H0, L0, dt
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H[0] = H0
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L[0] = L0
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for n in range(0, len(t)-1):
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H[n+1] = H[n] + a*dt*H[n] - b*dt*H[n]*L[n]
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L[n+1] = L[n] + d*dt*H[n]*L[n] - c*dt*L[n]
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return H, L, t
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# Load in data file
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data = np.loadtxt('Hudson_Bay.csv', delimiter=',', skiprows=1)
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# Make arrays containing x-axis and hares and lynx populations
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t_e = data[:,0]
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H_e = data[:,1]
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L_e = data[:,2]
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# Simulate using the model
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H, L, t = solver(m=20, H0=34.91, L0=3.857, dt=0.1,
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a=0.4807, b=0.02482, c=0.9272, d=0.02756,
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t0=1900)
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# Visualize simulations and data
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plt.plot(t_e, H_e, 'b-+', t_e, L_e, 'r-o', t, H, 'm--', t, L, 'k--')
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plt.xlabel('Year')
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plt.ylabel('Numbers of hares and lynx')
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plt.axis([1900, 1920, 0, 140])
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plt.title(r'Population of hares and lynx 1900-1920 (x1000)')
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plt.legend(('H_e', 'L_e', 'H', 'L'), loc='upper left')
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plt.savefig('Hudson_Bay_sim.pdf')
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plt.savefig('Hudson_Bay_sim.png')
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plt.show()
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