How to add random term in different steps of numerical integration - c++

Question

For the function below, I would not add the noise (Inoise in the code below) in every time step but, for example, only in every second time step. So while dt=0.0025 serves as the time step for the numerical integration, I would, for example, add Inoise only in every second time step (i.e. in 0.005 steps).
What is the best way to insert this into my existing function?
runs = 1000;
t_end = 5;
dt = 0.0025;
t_steps = t_end/dt;
for(int j=0; j<runs; j++){
double vT = v0;
double mT = m0;
double hT = h0;
double nT = n0;
for(int i=0; i<t_steps; i++){
double IStim = 0.0;
if ((delay / dt <= (double)i) && ((double)i <= (delay + duration) / dt))
IStim = I;
mT = (mT + dt * alphaM(vT)) / (1.0 + dt * (alphaM(vT) + betaM(vT)));
hT = (hT + dt * alphaH(vT)) / (1.0 + dt * (alphaH(vT) + betaH(vT)));
nT = (nT + dt * alphaN(vT)) / (1.0 + dt * (alphaN(vT) + betaN(vT)));
const double iNa = gNa * pow(mT, 3.0) * hT * (vT - vNa);
const double iK = gK * pow(nT, 4.0) * (vT - vK);
const double iL = gL * (vT-vL);
const double Inoise = (doubleRand() * knoise * sqrt(gNa * A));
const double IIon = ((iNa + iK + iL) * A) + Inoise;
vT += ((-IIon + IStim) / C) * dt;
voltage[i] = vT;
if(vT > 60.0) {
count++;
break;
}
}
}
return count;
}

Answer 1

You could accumulate the elapsed time and only add the noise once enough steps have passed:
double elapsedTime = 0;
double INoiseThreshold = 0.005;
for(int j=0; j<runs; j++){
//...
for(int i=0; i<t_steps; i++){
//...
double Inoise = 0;
elapsedTime += dt;
if(elapsedTime >= INoiseThreshold){
Inoise = (doubleRand() * knoise * sqrt(gNa * A));
elapsedTime = 0;
}
const double IIon = ((iNa + iK + iL) * A) + Inoise;
//...
}
}
return count;
Instead of comparing the floating point numbers directly, you could check if their differences are within an small epsilon to allow for rounding errors.
Instead of making the value of Inoise dependent on the condition, you could make the presence in the IIon formula dependent e.g.:
const double IIon = ((iNa + iK + iL) * A) + (elapsedTime >= INoiseThreshold) ? Inoise : 0;
just remember to reset elapsedTime once it surpassed the threshold.