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Matlab-Programs-for-Nonlinear-Dynamics/

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Matlab-Programs-for-Nonlinear-Dynamics/**repmut.m**

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%function repmut | |

% 12/08/14 | |

function repmut | |

clear | |

format compact | |

f = 1; % this is a dummy init to make f global | |

N = 64; % 64 | |

p = 1/sqrt(N); | |

time_expand = N; | |

mutype = 1; % 0 = Hamming 1 = rand | |

pay = 0; % 0 = Hamming 1 = 1/sqrt(N) | |

ep = .06; % average mutation rate: 0.1 to 0.01 typical (0.4835) | |

%%%%% Set original population | |

x0temp = rand(1,N); % Initial population | |

sx = sum(x0temp); | |

y0 = x0temp/sx; | |

Pop0 = sum(y0); | |

%%%%% Set Adjacency | |

%node = makeglobal(N); | |

node = makeER(N,0.1); | |

%node = makeSF(N,4); | |

%node = makeSW(N,4,0.5); | |

[Adj,degree,Lap] = adjacency(node); | |

%%%%%% Set Hamming distance | |

for yloop = 1:N | |

for xloop = 1:N | |

H(yloop,xloop) = hamming(yloop-1,xloop-1); | |

end | |

end | |

%%%%%%% Set Mutation matrix | |

if mutype == 0 | |

Qtemp = 1./(1+H/ep); %Mutation matrix on Hamming | |

%Qtemp = exp(-H/(ep*50)); | |

Qsum = sum(Qtemp,2); | |

% Normalize mutation among species | |

for yloop = 1:N | |

for xloop = 1:N | |

Q(yloop,xloop) = Qtemp(yloop,xloop)/Qsum(xloop); | |

end | |

end | |

elseif mutype == 1 | |

S = stochasticmatrix(N); | |

Stemp = S - diag(diag(S)); | |

Qtemp = ep*Stemp; | |

sm = sum(Qtemp,2)'; | |

Q = Qtemp + diag(ones(1,N) - sm); | |

end | |

figure(1) | |

imagesc(Q) | |

title('Mutation Matrix') | |

colormap(jet) | |

%%%%%%% Set payoff matrix | |

if pay == 1 | |

payoff = zeros(N,N); | |

for yloop = 1:N | |

payoff(yloop,yloop) = 1; | |

for xloop = yloop + 1:N | |

payoff(yloop,xloop) = p; | |

payoff(xloop,yloop) = p; | |

%payoff(yloop,xloop) = p*2*(0.5 - randbin(1,0.5)); | |

%payoff(xloop,yloop) = payoff(yloop,xloop); | |

%payoff(xloop,yloop) = -payoff(yloop,xloop); | |

end | |

end | |

elseif pay == 0 | |

payoff = exp(-1*H); | |

end | |

figure(2) | |

imagesc(payoff) | |

title('Payoff Matrix') | |

colormap(jet) | |

% Run time evolution | |

tspan = [0 1000]; | |

[t,x] = ode45(@quasispec,tspan,y0); | |

Pop0 | |

[sz,dum] = size(t); | |

Popend = sum(x(sz,:)) | |

phistar = sum(f.*x(sz,:)) % final average fitness | |

figure(3) | |

clf | |

h = colormap(lines); | |

for loop = 1:N | |

plot(t,x(:,loop),'Color',h(round(loop*64/N),:)) | |

hold on | |

end | |

hold off | |

figure(4) | |

clf | |

for loop = 1:N | |

semilogx(t,x(:,loop),'Color',h(round(loop*64/N),:)) | |

hold on | |

end | |

hold off | |

figure(5) | |

clf | |

for loop = 1:N | |

semilogy(t,x(:,loop),'Color',h(round(loop*64/N),:)) | |

hold on | |

end | |

hold off | |

%keyboard | |

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | |

% | |

% | |

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% | |

function yd = quasispec(~,y) | |

for loop = 1:N | |

ftemp(loop) = sum(payoff(:,loop).*y); | |

end | |

f = time_expand*ftemp/sum(ftemp); | |

% Transition matrix | |

for yloop = 1:N | |

for xloop = 1:N | |

W(yloop,xloop) = f(yloop)*(Adj(yloop,xloop)*Q(yloop,xloop)); | |

end | |

end | |

phi = sum(f'.*y); % Average fitness of population | |

yd = W*y - phi*y; | |

end % end quasispec | |

end | |