## Dynamic non-linear systems

Heard about the “Butterfly effect” ? I.e that a butterfly flapping its
wings in the Amazonas can create a storm on the other side of the
world…  An example of a complex system at play, at the “macro scale”.

Excellent introductions to complexity and non linear dynamic systems can be found in a couple of books, for instance the one by Melanie Mitchell I mentioned in a previous post, or Beinhocker’s  great book “Origin of wealth” (yes, that right, a book about finance, business &  money that’s actually interesting…!,  🙂 and way above most of the books you’d typically find on the shelves labelled “business & finance”, with typical title’s such as “Getting Rich  Fast for Dummies”… 🙂

A lot of the “systems” of the modern world, not least the socio-economic ones, i.e.  those involving human endeavor such as businesses and organizations – for instance  systems and software development –  are exhibiting complex system behavior, and should thus be managed as such, for instance by the “Steering analogy” suggested by Walker Royce, and not by the fully deterministic “command & control” planning philosophy most organizations of today, at least the large one’s, still prefer.

What I find so fascinating about these complex systems is for instance that a completely deterministic function, with no randomness what so ever in it – nor in its inputs – can generate totally different behavior when a single parameter is changed even so slightly.

As an example of a dynamic non-linear system, consider this almost trivial function (“Logistics map”), which can describe demographic models of the  evolution of a population in a resource constrained system:

B(n+1) <– r*(B(n) * (1-B(n) )

i.e. the next “season’s” population size is determined by a growth
factor (r) and the current season’s population size times the carrying-
capacity factor which is proportional to current population.

By modifying the value of the r parameter, the output of this function
takes very different forms, some of which stabilise around a fixed
anchor point, others with singular or multiple periods, and even fully
chaotic ones, i.e. those that do not stabilise at all!   You can find a good visualization of this function in this link:

http://en.wikipedia.org/wiki/Logistic_map

I entered this function into an Excel speadsheet and it just blew my
mind watching the graphs generated by different values of r!

The graphs below show four different runs, where the only variation point is the value of r.

In case you wonder what this has to do with system & software development or financial, business and organizational matters….?

I’d say a lot, but that’s a thread of it own… 🙂