m0 = 5000
d0 = 0.20.25
w0 = 1.00.95
\(\mu\) = 0.02190.024 m0 = 500200 d0 = 0.20.235 w0 = 1.00.99
Figure 5a, 5b 5c, 5d 5e, 5f 5g, 5h
State variables and their rates of change used for constraints State variables and their rates of change used for constraints State variables and their rates of change used for constraints State variables and their rates of change used for constraints State variables and their rates of change used for constraints
S 314.2 319.6 320.8 314.9
N 217962 144430 262537 166984
E 2.0380 x 107 1.7331 x 107 1.8280 x 107 1.7822 x 107
dS/dt -0.242 -0.009 0.0246 -0.196
dN/dt -418 -1052 2350 -758
dE/dt -4349 -112262 -48162 -88709
Lagrange multipliers Lagrange multipliers Lagrange multipliers Lagrange multipliers Lagrange multipliers
\(\lambda_{1}\) 0.00047481 0.0026949 -0.0059150 0.0015918
\(\lambda_{2}\) 0.000014104 7.8932 x 10-6 0.000047504 0.000011608
\(\lambda_{3}\) 0.10275 0.19247 0.46754 0.18211
\(\lambda_{4}\) -0.000028926 -0.00023261 0.00040369 -0.00013171
\(\lambda_{5}\) 0.0025553 -0.0091482 -0.22996 -0.0032439