# Matlab:Refined population model

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% % REFINED MAGICAL GIRL-WITCH POPULATION MODEL % BASIC MAGICAL GIRL-WITCHES MODEL % This file has been produced for Matlab 7.4.0 % It is 100% compatible with FreeMat 4.0, however, you may want to change the plot commands to % plot(M, 'g.-') and plot(W, 'r.-') for aesthetics purpose % % % If you want to modify the constants, please bear these restrictions in mind: % -C should be an integer % -D, B, F, K should be values in [0,1] % -B should be greater than K (or else, the number of witches will be negative) % -W(1) should be strictly positive. If W(1)=0, no witch appear ever, and MSes grow linearily % C = 100; % Number of girls contracted by QBe D = 0.200; % Proportion of girls (who are fighting) that die B = 0.100; % Proportion of girls (who are fighting) to become witches F = 0.015; % Proportion of familiars becoming witches K = 0.096; % Proportion of witches getting killed by MSes steps = 500; % Number of iterations for the simulation M(1) = 0; % Number of magical girls at first W(1) = 1; % Number of witches at first hold on for t=1:steps prop = min(M(t), W(t)); deltaM = C- prop*(D+B); deltaW = F*W(t) + prop*(B-K); M(t+1)=M(t)+deltaM; W(t+1)=W(t)+deltaW; end title('Evolution of the Magical Girls population over time') xlabel('time') ylabel('number of magical girls/witches') plot(M, 'g-') plot(W, 'r-') legend('Magical Girls', 'Witches', 'location', 'northeast') legend('boxoff') hold off