How do I specify which reaction is next in the First Reaction Method?

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Evan 2014-3-11

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https://ww2.mathworks.cn/matlabcentral/answers/120969-how-do-i-specify-which-reaction-is-next-in-the-first-reaction-method

I'm evaluating a set of reactions (Brusselator Reactions) with the Direct Method (DM) and First Reaction Method (FRM) of the Gillespie Algorithm. While calculating with the DM was relatively straight forward, I'm having trouble understanding how to update my quantities of reagents given the smallest time step.

Given this set of update rules from the DM for this system:

while N<tstop
      N=N+1;
      s1=rand;
      tnext=(1/a)*log(1/(1-s1));
      T=T+tnext;
      s2=rand*P4;
      decision=zeros(4,1);
      decision(1)= s2<=P1;
      decision(2)=(s2>P1)&&(s2<=P2);
      decision(3)=(s2>P2)&&(s2<=P3);
      decision(4)=(s2>P3)&&(s2<=P4);
      X1=X1-decision(1)-decision(2);
      X2=X2-decision(2);
      Y1=Y1+3*decision(3)-decision(2)-2*decision(3)-decision(4);
      Y2=Y2+decision(2)-decision(3);
      Z1=Z1+decision(2);
      Z2=Z2+decision(4);
end

And this selection for the smallest time step in the FRM:

a=[a1 a2 a3 a4];
...
while N<simstps
      N=N+1;
      s=rand(4,1);    
      tnext=(1./a).*log(1./(1-s));
      [a,b]=find(min(tnext));
      T=T+tnext(a,b);
end