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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) Rab its Foxes 0 10 10 0.1 10 9.97 0.2 10.0 03 9.940 9 0.3 10.0 089 9.91027 where the parameters are definded by: 0.4 10.0 1796 9.8 05401 t= time in days 0.5 10.0 29 1 9.85090 3 a= 0.1 the natural growth rate of rab its in the absence of preditation (foxes) 0.6 10.0 4 83 9.8213505 b= 0.01 the rab it death rate per encounter of rab its and foxes 0.7 10.0 627 9.7918909 c= 0.04 the natural death rate of foxes in the absence of fo d (rab its) 0.8 10.0 8352 9.7625213 d= 0.1 the ef iciency of turning eaten rab its into foxes 0.9 10.010729 9.73 2419 1 10.0134 9.7040526 1.1 10.016363 9.6749535 Maximum rab its= 106.05129 1.2 10.019619 9.64594 5 Minimum rab its= 9.6507903 1.3 10.02316 9.617025 1.4 10.0270 5 9.58 1967 Maximum Foxes= 19.32 817 1.5 10.031 34 9.5 9458 Minimum Foxes= 4.3487623 1.6 10.035 53 9.5308094 1.7 10.040262 9.502 509 1.8 10.045259 9.4737824 1.9 10.050545 9.4 54039 2 10.0561 9 9.4171 5 2.1 10.061981 9.38 917 2.2 10.06813 9.3608084 2.3 10.074565 9.3 27898 2.4 10.081287 9.304861 2.5 10.08 295 9.27 02 delta t R max R min F max F min 2.6 10.095 8 9.2492729 2.7 10.103168 9.2 16135 2.8 10.1 1032 9.1940438 2.9 10.1 9181 9.16 5637 3 10.127614 9.139173 3.1 10.1363 3 9.1 18724 3.2 10.1453 5 9.0846 1 3.3 10.154621 9.057539 3.4 10.164192 9.0305065 3.5 10.174046 9.0 35632 3.6 10.184184 8.9767092 3.7 10.194605 8.949 4 4 3.8 10.20531 8.923268 3.9 10.216298 8.896 82 4 10.2 757 8.8701846 4.1 10.239125 8.8437 59 4.2 10.250964 8.817456 4.3 10.263086 8.7912 49 4.4 10.275492 8.7650825 4.5 10.28 181 8.739028 4.6 10.301 5 8.7130635 4.7 10.314 1 8.6871867 4.8 10.327952 8.6 13983 4.9 10.3417 7 8.6356982 5 10.35 8 7 8.610 862 5.1 10.37028 8.5845624 5.2 10.384959 8.5 9126 5.3 10.39 92 8.53 7 87 5.4 10.415171 8.5085186 5.5 10.430705 8.483 463 5.6 10.4 6525 8.4582617 5.7 10.462631 8.43 2646 5.8 10.479023 8.4083549 5.9 10.495702 8.3835326 6 10.5126 8 8.3587976 6.1 10.529 21 8.3 41497 6.2 10.547462 8.30958 9 6.3 10.565292 8.2851 51 6.4 10.58341 8.2607281 6.5 10.601817 8.2364278
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