how to generate (multiple) realisations using Gillespie Algorithms

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yamen alharbi 2020-12-24

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https://ww2.mathworks.cn/matlabcentral/answers/701782-how-to-generate-multiple-realisations-using-gillespie-algorithms

评论： yamen alharbi 2021-1-3

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Hello, I would like to simulate this reaction

a->X

X-> X

at rates c. here is a code was written by Desmond Higham and I tried to adopted it to this reaction.

I would like to simulate different realisations . Could you please shed a light on this.

Your help is highly aprrecaited.

clf
clear all;
clc
rand('state',100)
%stoichiometric matrix
V = [1 -1];
%%%%%%%%%% Parameters and Initial Conditions %%%%%%%%%
nA = 6.023e23;             % Avagadro's number
vol = 1e-15;               % volume of system
X = zeros(1,1);
X(1) = 100; % molecules of substrate
c(1) = .4; c(2) =.1; c(3)=8; c(4)=.3;
t = 0;
tfinal = 100;
count = 1;
tvals(1) = 0;
Xvals(:,1) = X;
while t < tfinal
     a(1) = c(1);% calculate propensity functions
     a(2) = c(2)*X(1);
     asum = sum(a); 
     j = min(find(rand<cumsum(a/asum))); % select which reaction
     tau = log(1/rand)/asum; % select time
     X = X + V(:,j); %update X
    
     count = count + 1;
     t = t + tau; %Update time
     tvals(count) = t;
     Xvals(:,count) = X;
end
%%%%%%%%%%% Plots %%%%%%%%
L = length(tvals);
tnew = zeros(1,2*(L-1));
tnew(1:2:end-1) = tvals(2:end);
tnew(2:2:end) = tvals(2:end);
tnew = [tvals(1),tnew];
% 
Svals = Xvals(1,:);
ynew = zeros(1,2*L-1);
ynew(1:2:end) = Svals;
ynew(2:2:end-1) = Svals(1:end-1);
plot(tnew,ynew,'g-')
hold on

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Star Strider 2021-1-3

The only one that appears to be accessable is the SIAM paper. I’ll download it now and read it later. (The first is behind a paywall, the second offers only short descriptions and no links to other information.)

yamen alharbi 2021-1-3