How long until the blue/fin whale populations stabilize if B(0)=5000B(0) = 5000B(0)=5000 and F(0)=70000F(0) = 70000F(0)=70000
Variables B=B =B= Number of blue whales F=F =F= Number of fin whales
Assumptions ΔB=0.05B(1−B150000)−αBF\Delta B = 0.05B(1-\frac{B}{150000})-\alpha B FΔB=0.05B(1−150000B)−αBF ΔF=0.08F(1−F400000)−αBF\Delta F = 0.08F(1-\frac{F}{400000})-\alpha B FΔF=0.08F(1−400000F)−αBF
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)
