Posted in the past harrytrader 02-07-03 05:28 PM
http://www.elitetrader.com/vb/showthread.php?s=&postid=200167&highlight=non+linear#post200167
About non-linearity, well the term can have different sense depending on the context, for example many people think that non linearity means that a model is just different from a straight line. But in the context of chaos theory, a model that does not give a straight line isn't necessarily non linear. To really understand I need to write that a linear model can be writen
x[n+1]=a*x[n]+b where a and b are parameters (not dependant on time whereas x is a variable whose value depends on time n)
You will remark the iterative form definition above.
For example the interest compounding is linear since
S[n+1] = S[n]*(1+r) where r is the interest rate (here b=0)
when a > 1 this give not a straight line and there is no limit to S which can tend to infinite !
A non linear model cannot be written as above. the most well known and studied is the logistic function where you "dump" the infinite growth of a*x[n] by a new term (x[n]-1) so that the growth is finite and cannot go higher than Xmax.
In that case you will have different behavior:
If a = 0 x will tend towards 0: it is the attraction point
If 1 < a < 3 the attraction point will depend upon a
When a > 3 you will have 2 or more attractions points. this is called bifurcation and give the image of a system be chaotic.
Quote from rlb21079:
A basic linear function looks like, y = mx + b.
What does a non-linear function look like?
