from scipy.integrate import odeint
from pylab import * # for plotting commands
    
def LV_deriv(y,t,alfa):
    u = y[0]
    v= y[1]
    du = u*(1-v)
    dv = alfa*v*(u-1)
    return array([du, dv])
    
time = linspace(0.0,100.0,100000) 
yinit = array([1.01,1.01]) # initial values 
a = 2.0
for i in range(1):
    y = odeint(LV_deriv,yinit+i*0.1,time, args =(a,),atol=1e-13,rtol = 1e-13)
    figure(1) 
    plot(time,y[:,0]) # y[:,0] is the first column of y 
    plot(time,y[:,1])
    xlabel('t') 
    ylabel('y') 
    figure(2)
    plot(y[:,0],y[:,1]) # y[:,0] is the first column of y 
show()