Kernel: Python 3 (system-wide)
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import matplotlib.pyplot as plt from numpy import arange
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alpha = 0.5471 beta = 0.0481 gamma = 0.001 def f(x,t): return alpha*x - beta*x*t - gamma*x**2 a, b = 0.0, 60.0 N = 1000 h = 0.0001 x = 1.0 tpoints = arange(a, b, h) rk4_xpoints = [] for t in tpoints: rk4_xpoints.append(x) k1 = h*f(x, t) k2 = h*f(x+0.5*k1, t+0.5*h) k3 = h*f(x+0.5*k2, t+0.5*h) k4 = h*f(x+k3, t+h) x += (k1+2*k2+2*k3+k4)/6.0 plt.plot(tpoints, rk4_xpoints, label="RK4 depredador") plt.xlabel("$t$") plt.ylabel("$x(t)$") plt.legend() plt.show()
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delta = 0.0466 epsilon = 0.8439 zeta = 0.001 def f(x,t): return delta*t*x - epsilon*x - zeta*x**2 a, b = 0.0, 60.0 N = 1000 h = 0.0001 x = 1.0 tpoints = arange(a, b, h) rk4_xpoints = [] for t in tpoints: rk4_xpoints.append(x) k1 = h*f(x, t) k2 = h*f(x+0.5*k1, t+0.5*h) k3 = h*f(x+0.5*k2, t+0.5*h) k4 = h*f(x+k3, t+h) x += (k1+2*k2+2*k3+k4)/6.0 plt.plot(tpoints, rk4_xpoints, label="RK4 presa") plt.xlabel("$t$") plt.ylabel("$x(t)$") plt.legend() plt.show()
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alpha = 0.5471 beta = 0.0481 gamma = 0.001 def f(x,t): return alpha*x - beta*x*t - gamma*x**2 a, b = 0.0, 20.0 N = 1000 h = 0.0001 x = 60.0 tpoints = arange(a, b, h) rk4_xpoints = [] for t in tpoints: rk4_xpoints.append(x) k1 = h*f(x, t) k2 = h*f(x+0.5*k1, t+0.5*h) k3 = h*f(x+0.5*k2, t+0.5*h) k4 = h*f(x+k3, t+h) x += (k1+2*k2+2*k3+k4)/6.0 delta = 0.0466 epsilon = 0.8439 zeta = 0.001 def g(y,t): return delta*t*y - epsilon*y - zeta*y**2 a, b = 0.0, 20.0 N = 1000 h = 0.0001 y = 60.0 tpoints = arange(a, b, h) rk4_ypoints = [] for t in tpoints: rk4_ypoints.append(y) k1 = h*g(y, t) k2 = h*g(y+0.5*k1, t+0.5*h) k3 = h*g(y+0.5*k2, t+0.5*h) k4 = h*g(y+k3, t+h) y += (k1+2*k2+2*k3+k4)/6.0 plt.plot(tpoints, rk4_xpoints, label="RK4 depredador") plt.xlabel("$x(t)$") plt.ylabel("$t$") plt.plot(tpoints, rk4_ypoints, label="RK4 presa") plt.xlabel("$t$") plt.ylabel("$y(t)$") plt.legend() plt.show()
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alpha = 0.5471 beta = 0.0481 gamma = 0.001 delta = 0.0466 epsilon = 0.8439 zeta = 0.001 s = [x, y] def f(x,y): return s a, b = 0.0, 60.0 N = 1000 h = 0.0001 x = alpha*x - beta*x*t - gamma*x**2 y = delta*t*y - epsilon*y - zeta*y**2 tpoints = arange(a, b, h) rk4_xpoints = [] for t in tpoints: rk4_xpoints.append(x) k1 = h*f(x, t) k2 = h*f(x+0.5*k1, t+0.5*h) k3 = h*f(x+0.5*k2, t+0.5*h) k4 = h*f(x+k3, t+h) x += (k1+2*k2+2*k3+k4)/6.0 plt.plot(tpoints, rk4_xpoints, label="RK4") plt.xlabel("$t$") plt.ylabel("$x(t)$") plt.legend() plt.show()
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---------------------------------------------------------------------------
NameError Traceback (most recent call last)
/tmp/ipykernel_538/3464085761.py in <cell line: 7>()
5 epsilon = 0.8439
6 zeta = 0.001
----> 7 s = [x, y]
8
9 def f(x,y): return s
NameError: name 'x' is not defined
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alpha = 0.5471 beta = 0.0481 gamma = 0.001 def f(x,t): return alpha*x - beta*x*t - gamma*x**2 a, b = 0.0, 60.0 N = 1000 h = 0.0001 x = 1.0 tpoints = arange(a, b, h) rk4_xpoints = [] for t in tpoints: rk4_xpoints.append(x) k1 = h*f(x, t) k2 = h*f(x+0.5*k1, t+0.5*h) k3 = h*f(x+0.5*k2, t+0.5*h) k4 = h*f(x+k3, t+h) x += (k1+2*k2+2*k3+k4)/6.0 delta = 0.0466 epsilon = 0.8439 zeta = 0.001 def g(y,t): return delta*t*y - epsilon*y - zeta*y**2 a, b = 0.0, 60.0 N = 1000 h = 0.0001 y = 1.0 tpoints = arange(a, b, h) rk4_ypoints = [] for t in tpoints: rk4_ypoints.append(y) k1 = h*g(y, t) k2 = h*g(y+0.5*k1, t+0.5*h) k3 = h*g(y+0.5*k2, t+0.5*h) k4 = h*g(y+k3, t+h) y += (k1+2*k2+2*k3+k4)/6.0 plt.plot(tpoints, rk4_xpoints, label="RK4 depredador") plt.xlabel("$t$") plt.ylabel("$x(t)$") plt.plot(tpoints, rk4_ypoints, label="RK4 presa") plt.xlabel("$t$") plt.ylabel("$y(t)$") plt.legend() plt.show()
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alpha = 0.5471 beta = 0.0481 gamma = 0.001 delta = 0.0466 epsilon = 0.8439 zeta = 0.001 def f(x,t): return alpha*x - beta*x*t - gamma*x**2 def g(y,t): return delta*t*y - epsilon*y - zeta*y**2 a, b = 0.0, 60.0 N = 1000 h = 0.0001 x = 1.0 y = 1.0 tpoints = arange(a, b, h) rk4_xpoints = [] rk4_ypoints = [] for t in tpoints: rk4_xpoints.append(x) rk4_ypoints.append(y) k1 = h*f(x, t) k1 = h*g(y, t) k2 = h*f(x+0.5*k1, t+0.5*h) k2 = h*g(y+0.5*k1, t+0.5*h) k3 = h*f(x+0.5*k2, t+0.5*h) k3 = h*g(y+0.5*k2, t+0.5*h) k4 = h*f(x+k3, t+h) k4 = h*g(y+k3, t+h) x += (k1+2*k2+2*k3+k4)/6.0 y += (k1+2*k2+2*k3+k4)/6.0 plt.plot(tpoints, rk4_xpoints, label="RK4 depredador") plt.plot(tpoints, rk4_ypoints, label="RK4 presa") plt.legend() plt.show(f,g)
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alpha = 0.5471 beta = 0.0481 gamma = 0.001 delta = 0.0466 epsilon = 0.8439 zeta = 0.001 def f(x,t): return alpha*x - beta*x*t - gamma*x**2 def g(y,t): return delta*t*y - epsilon*y - zeta*y**2 a, b = 0.0, 60.0 N = 1000 h = 0.0001 x = 1.0 y = 1.0 plt.show(f,g)
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