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Kernel: SageMath 7.6

Whale problem simulation... again (╯°□°）╯︵ ┻━┻

How long until the blue/fin whale populations stabilize if B(0)=5000B(0) = 5000 and F(0)=70000F(0) = 70000

Variables B=B = Number of blue whales F=F = Number of fin whales

Assumptions ΔB=0.05B(1−B150000)−αBF\Delta B = 0.05B(1-\frac{B}{150000})-\alpha B F ΔF=0.08F(1−F400000)−αBF\Delta F = 0.08F(1-\frac{F}{400000})-\alpha B F

B0 = 5000
F0 = 70000
a = 10^(-7)
t = 37

f1(B,F) = 0.05*B*(1-B/150000) - a*B*F
f2(B,F) = 0.08*F*(1-F/400000) - a*B*F

L_B = [B0]
L_F = [F0]

for i in range(100):
    B_next = L_B[-1] + f1(L_B[-1],L_F[-1])*t
    F_next = L_F[-1] + f2(L_B[-1],L_F[-1])*t
    L_B.append(B_next)
    L_F.append(F_next)
    
p1 = list_plot(L_B)
p2 = list_plot(L_F, color="fuchsia")
show(p1+p2)