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Homework 12

# Homework 12 - deltat= 0.1 dR/dt= R(a-b*F)= a*R-b*R*F...

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deltat= 0.1 dR/dt= R* (a-b*F)= a*R-b*R*F dF/dt= -F*(c-d*b*R)= d*b*R*F-c*F Euler's Solution t(days) Rabbits Foxes 0 10 10 0.1 10 9.97 0.2 10.0003 9.94009 0.3 10.000899 9.91027 where the parameters are definded by: 0.4 10.001796 9.8805401 t= time in days 0.5 10.002991 9.8509003 a= 0.1 the natural growth rate of rabbits in the absence of preditation (foxes) 0.6 10.004483 9.8213505 b= 0.01 the rabbit death rate per encounter of rabbits and foxes 0.7 10.00627 9.7918909 c= 0.04 the natural death rate of foxes in the absence of food (rabbits) 0.8 10.008352 9.7625213 d= 0.1 the efficiency of turning eaten rabbits into foxes 0.9 10.010729 9.7332419 1 10.0134 9.7040526 1.1 10.016363 9.6749535 Maximum rabbits= 106.05129 1.2 10.019619 9.6459445 Minimum rabbits= 9.6507903 1.3 10.023166 9.6170255 1.4 10.027005 9.5881967 Maximum Foxes= 19.322817 1.5 10.031134 9.559458 Minimum Foxes= 4.3487623 1.6 10.035553 9.5308094 1.7 10.040262 9.5022509 1.8 10.045259 9.4737824 1.9 10.050545 9.4454039 2 10.056119 9.4171155 2.1 10.061981 9.388917 2.2 10.06813 9.3608084 2.3 10.074565 9.3327898 2.4 10.081287 9.304861 2.5 10.088295 9.277022 delta t R max R min F max F min 2.6 10.095588 9.2492729 2.7 10.103168 9.2216135 2.8 10.111032 9.1940438 2.9 10.119181 9.1665637 3 10.127614 9.1391733 3.1 10.136333 9.1118724 3.2 10.145335 9.084661 3.3 10.154621 9.057539 3.4 10.164192 9.0305065 3.5 10.174046 9.0035632 3.6 10.184184 8.9767092 3.7 10.194605 8.9499444 3.8 10.20531 8.9232688 3.9 10.216298 8.8966822 4 10.22757 8.8701846 4.1 10.239125 8.8437759 4.2 10.250964 8.817456 4.3 10.263086 8.7912249 4.4 10.275492 8.7650825 4.5 10.288181 8.7390288 4.6 10.301155 8.7130635 4.7 10.314411 8.6871867 4.8 10.327952 8.6613983 4.9 10.341777 8.6356982 5 10.355887 8.6100862 5.1 10.37028 8.5845624 5.2 10.384959 8.5591266 5.3 10.399922 8.5337787 5.4 10.415171 8.5085186 5.5 10.430705 8.4833463 5.6 10.446525 8.4582617 5.7 10.462631 8.4332646 5.8 10.479023 8.4083549 5.9 10.495702 8.3835326 6 10.512668 8.3587976 6.1 10.529921 8.3341497 6.2 10.547462 8.3095889 6.3 10.565292 8.2851151 6.4 10.58341 8.2607281 6.5 10.601817 8.2364278 6.6 10.620515 8.2122142 6.7 10.639502 8.1880872 6.8 10.65878 8.1640466 6.9 10.678349 8.1400922 7 10.698209 8.1162241 7.1 10.718362 8.0924422 7.2 10.738808 8.0687462 7.3 10.759548 8.0451361 7.4 10.780581 8.0216117 7.5 10.801909 7.998173 7.6 10.823533 7.9748199 7.7 10.845452 7.9515522 7.8 10.867669 7.9283698 7.9 10.890183 7.9052726 8 10.912995 7.8822605 8.1 10.936105 7.8593334 8.2
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