from scitools.std import *

def ex_FishShark(F0,S0,T,dt):
    """Explicit numerical solution of  
       F'(t)=(2-S(t))F(t), F(0)=F0, 
       S'(t)=(F(t)-1)S(t), S(0)=S0, 
       for 0<t<T and with time step dt. 
    """ 

    times=arange(0,T+dt,dt)
    N=len(times)

    F=zeros(N) # Fish population
    S=zeros(N) # Shark population
    
    F[0]=F0
    S[0]=S0

    # Compute numerical approximations
    for n in range(N-1): 
        F[n+1]= F[n]+dt*(2-S[n])*F[n]
        S[n+1]= S[n]+dt*(F[n]-1)*S[n] 


    # Standard plotting
    plot(times,F)
    hold('on')
    plot(times,S)
    xlabel('t')
    ylabel('population')
    legend('Fish','Shark')
   
    hold('off') 
    
    # Plotting in Phase plane
    # plot(F,S)   
    # xlabel('F')
    # ylabel('S')