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--- 2016:groups:g1:start [2016/01/09 23:22] – group1
+++ 2016:groups:g1:start [2024/01/09 18:45] (current) – external edit 127.0.0.1
@@ Line 2: / Line 2: @@
 ====== Less is more: when positives don't sum ======
+==== Plot 1 ====
+%matplotlib inline
+from numpy import *
+from matplotlib.pyplot import *
+from scipy.integrate import odeint
+ion()
+t = arange(0,2., 0.01)
+# parameters
+fr = 8.75
+fa = 6.25
+p = 0.7
+c = 0.01
+g = 0.001
+# initial condition: this is an array now!
+x0 = array([10., 10.]) # Pr, Pa
+# the function still receives only `x`, but it will be an array, not a number
+def LV(x, t, fr, fa, p, c, g):
+    # in python, arrays are numbered from 0, so the first element
+    # is x[0], the second is x[1]. The square brackets `[ ]` define a
+    # list, that is converted to an array using the function `array()`.
+    # Notice that the first entry corresponds to dV/dt and the second to dP/dt
+    return array([ (fr*p*x[0]) + fa*p*x[1] - ((c-g)*x[0]*(x[0]+x[1])),
+                   (fa*(1-p)*x[1]) + fr*(1-p)*x[0] - ((c-3*g)*x[1]*(x[0]+x[1])) ])
+# call the function that performs the integration
+# the order of the arguments is as below: the derivative function,
+# the initial condition, the points where we want the solution, and
+# a list of parameters
+x = odeint(LV, x0, t, (fr, fa, p, c, g))
+# plot the solution
+plot(t, x)
+xlabel('$t [years^{-1}]$', fontsize=25) # define label of x-axis
+ylabel('$Plants Population$', fontsize=25) # and of y-axis
+legend(['$P_{r}$', '$P_{a}$'], loc='lower right', fontsize=20)
+savefig('foo1.pdf')
 ==== Portuguesa ====
 t = arange(0,3., 0.01)