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Path: 6.7.ipynb
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Kernel: SageMath 10.1
alpha = 1*10^(-8)
x0=5000
y0=70000
c=3000

f(x,y)= 0.05*x*(((x-c)*(1-(x/150000)))/(x+c))-alpha*x*y
g(x,y) = 0.08*y*(((y-15000)*(1-(y/400000)))/(y+15000))-alpha*x*y

streams=streamline_plot((f(x,y),g(x,y)), (x,0,400000),(y,0,500000))
display(streams)
whale_war=[]
deltat=1
Ev=0
while Ev <= 100:
    data=[[0,x0,y0]]  #initial (t,x,y)
    t=0
    x=x0
    y=y0
    for i in range(10000):
        deltax=f(x,y)*deltat
        deltay=g(x,y)*deltat
        t+=deltat
        x+=deltax
        y+=deltay
        data.append([t,x,y])
        if abs(deltax) < .5 and abs(deltay) < .5:
            whale_war.append([c, t, x, y])
            break
            
    Ev+=1000

display(table(whale_war))
Image in a Jupyter notebook

It takes 331 days to reach equilibrium and the whales do not wipe eachother out 😃

alpha = 1*10^(-8)
x0=5000
y0=70000
c=1000

f(x,y)= 0.05*x*(((x-c)*(1-(x/150000)))/(x+c))-alpha*x*y
g(x,y) = 0.08*y*(((y-15000)*(1-(y/400000)))/(y+15000))-alpha*x*y



deltat=1
Ev=0
while Ev <= 100:
    data=[[0,x0,y0]]  #initial (t,x,y)
    t=0
    x=x0
    y=y0
    for i in range(10000):
        deltax=f(x,y)*deltat
        deltay=g(x,y)*deltat
        t+=deltat
        x+=deltax
        y+=deltay
        data.append([t,x,y])
        if abs(deltax) < .5 and abs(deltay) < .5:
            whale_war.append([c, t, x, y])
            break
            
    Ev+=1000



alpha = 1*10^(-8)
x0=5000
y0=70000
c=2000

f(x,y)= 0.05*x*(((x-c)*(1-(x/150000)))/(x+c))-alpha*x*y
g(x,y) = 0.08*y*(((y-15000)*(1-(y/400000)))/(y+15000))-alpha*x*y



deltat=1
Ev=0
while Ev <= 100:
    data=[[0,x0,y0]]  #initial (t,x,y)
    t=0
    x=x0
    y=y0
    for i in range(10000):
        deltax=f(x,y)*deltat
        deltay=g(x,y)*deltat
        t+=deltat
        x+=deltax
        y+=deltay
        data.append([t,x,y])
        if abs(deltax) < .5 and abs(deltay) < .5:
            whale_war.append([c, t, x, y])
            break
            
    Ev+=1000


alpha = 1*10^(-8)
x0=5000
y0=70000
c=4000

f(x,y)= 0.05*x*(((x-c)*(1-(x/150000)))/(x+c))-alpha*x*y
g(x,y) = 0.08*y*(((y-15000)*(1-(y/400000)))/(y+15000))-alpha*x*y



deltat=1
Ev=0
while Ev <= 100:
    data=[[0,x0,y0]]  #initial (t,x,y)
    t=0
    x=x0
    y=y0
    for i in range(10000):
        deltax=f(x,y)*deltat
        deltay=g(x,y)*deltat
        t+=deltat
        x+=deltax
        y+=deltay
        data.append([t,x,y])
        if abs(deltax) < .5 and abs(deltay) < .5:
            whale_war.append([c, t, x, y])
            break
            
    Ev+=1000



alpha = 1*10^(-8)
x0=5000
y0=70000
c=5000

f(x,y)= 0.05*x*(((x-c)*(1-(x/150000)))/(x+c))-alpha*x*y
g(x,y) = 0.08*y*(((y-15000)*(1-(y/400000)))/(y+15000))-alpha*x*y



deltat=1
Ev=0
while Ev <= 100:
    data=[[0,x0,y0]]  #initial (t,x,y)
    t=0
    x=x0
    y=y0
    for i in range(10000):
        deltax=f(x,y)*deltat
        deltay=g(x,y)*deltat
        t+=deltat
        x+=deltax
        y+=deltay
        data.append([t,x,y])
        if abs(deltax) < .5 and abs(deltay) < .5:
            whale_war.append([c, t, x, y])
            break
            
    Ev+=1000



alpha = 1*10^(-8)
x0=5000
y0=70000
c=6000

f(x,y)= 0.05*x*(((x-c)*(1-(x/150000)))/(x+c))-alpha*x*y
g(x,y) = 0.08*y*(((y-15000)*(1-(y/400000)))/(y+15000))-alpha*x*y


deltat=1
Ev=0
while Ev <= 100:
    data=[[0,x0,y0]]  #initial (t,x,y)
    t=0
    x=x0
    y=y0
    for i in range(10000):
        deltax=f(x,y)*deltat
        deltay=g(x,y)*deltat
        t+=deltat
        x+=deltax
        y+=deltay
        data.append([t,x,y])
        if abs(deltax) < .5 and abs(deltay) < .5:
            whale_war.append([c, t, x, y])
            break
            
    Ev+=1000
header=["c","t","x","y"]
display(table(whale_war, header_row=header))

I would say there is a lot of sensitivity because if you look after c=4000 the population switches to a different equilibrium point which is where one of the whale populations cease to exist 😦

sorry for so much code I spent an hour and a half trying to put this into a loop and it wouldnt run