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- Summary:
- I have 14 coupled ordinary differential equations. I am trying to increase the concentration of one of the ODEs by adding a sinusoidal equation that is at the same time "noisy". This noise I introduce follows a gaussian distribution with mean 0 and sigma that I vary in several experiments. I have not tried calculating for an analytical solution (not sure if even possible) but only used Python to solve the system. I don't know if I am doing it right. Any help is appreciated.

**The Coupled ODE Model**

Below are my coupled differential equations, where the only variable I try to meddle with is the ITM

_{blood}. The motivation here is if I try to increase ITM

_{blood}(in the next section I will show how I do it), at some concentration of ITM

_{blood}(most likely a very huge one) , the system below "collapses." That is, some of the concentrations just flattens out.

**Introducing Noise to ITM**

_{blood}This is just a naive method that I am doing. So I just add a "

**source**" of this ITM

_{blood}that follows a sinusoidal function which plateaus at r

_{ITMaddpeak}and somehow starts "late" controlled by t

_{ITMadd}. Then I add "

**noise"**that simply follows a gaussian distribution with mu = 0 and sigma that I vary as part of my experiments.

**Python Library Used to Solve the Equations**

scipy.integrate.odeint

note: I have tried an existing library (sdeint) specifically designed for SDEs but for some reason, the solver just can't handle the system/blows up, even when I have not added noise yet (used this as sanity check).

Am I doing this right? Does this method of introducing noise make sense? Thank you very much! I can upload my notebooks if necessary.

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