Matlab:New population model

Script

%
% NEW 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
%


I = 0.25;    % Number of girls contracted by Kyubey, depending on the number of witches
B = 0.125;   % Proportion of girls becoming witches, per iteration
F = 0.015;   % Proportion of familiars maturing into witches, per iteration
D = 0.001;   % Proportion of Magical Girls getting killed, either by witches or by other MSes
H = 0;       % Average heroism of Magical Girls (i.e. number of familiars they fight)
K = 0.12;    % Number of witches getting killed by Magical Girls

steps = 100; % Number of iterations for the simulation

M(1) = 10;    % Number of magical girls at first
W(1) = 0;    % Number of witches at first

hold on

for t=1:steps
    deltaM = I*W(t) - B*M(t) - D*M(t)*W(t);
    deltaW = B*M(t) + F*(W(t) - H*M(t)) - K*M(t)*W(t);
    
    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 

Notes

• Results are dumped on the talkpage (graphs and sets of values used)
• This model is still a work in progress. Do not take it as granted yet