|Feb10-12, 07:13 AM||#1|
Pertubance in a model
Long story short:
I'm writing a project om modelling cellular aging in biological tissue from the principle that cells have to stay alive as long as possible without help from stem cells (biophysics).
Now the model of the amount of cells fluctuates around a steady state until stochastic fluctuations make it decline rapidly.
To describe this (I think) my article introduces something called pertubations. What are they, would it be possible that they were used to describe stochastic behaviour, and does anyone know a good link to read about them? :)
|Feb12-12, 01:08 PM||#2|
Since any experimental alteration in a stable system for the purpose of studying the effect is a very general and widely used tool, I don't think a specific reference is going to be of much use except as an example. Your own experimental model would seem to be such an example. The general idea is to disturb the system just enough to measure some effect without causing the system to break down. Measuring how robust a system is under deformation, seeing how long it will take to re-establish its equilibrium or some new equilibrium, and by what means are some objectives of perturbative methods and theory.
|Feb12-12, 04:23 PM||#3|
In nonlinear dynamics of biology, we would treat the homeostatic point as a "stable focus" and the threshold beyond which the system fails us would be an "unstable limit cycle". It is basically a dot in the middle of a circle. The dot attracts solutions towards it, the circle pushes solutions away from it (so solutions inside the circle get smaller, solutions outside get bigger). Imagining the potential energy analogy, it would mean that you basically have a huge bowl inside of a mountain with a ball in it. Small perturbations of the ball inside the bowl, and it just comes back to the bottom of the bowl, but a sufficient perturbation and you knock the ball over the walls of the bowl and it flies faster and faster down the mountain outside, until it reaches the bottom, at a much lower state than the bottom of the bowl (having significant biological effects in the whole organism).
There's actually a slight difference with the mountain analogy. Solutions don't have to swirl around as the approach the point. In biological systems, we are generallly plotting two variables against each other that do make a deterministic cycle, so the motion will be circular like in the flow diagram.
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