|Thanks for the ideas. To a certain extent, I'm not really sure how to parameterize my question to even go on from there. I have in my head graphs of information entropy for my two systems and how I envision they overlap, but I'm trying to figure out 1: how to establish relationships of dominance and 2: what the level of dominance needs to be for one structure to be abandoned or overcoded. I know it can't be a simple issue of one system has a higher connectivity to its center than the other does because there will be an issue of inertia in the system. There will have to be an amount of extra connection to serve as the activation energy for the flip. |
For the second issue, I have an analogy in my head that consists of two light sources facing each other that cast shadows of an object between them:
` /` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `\
|(~O ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` O~)|
| \` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` `/`|
| ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` ` |
| ` ` ` ` ` ` ` ` `_` ` ` ` ` ` ` ` ` `|
|` ` ` ` ` ` ` `__| |__` ` ` ` ` ` ` ` |
(I did this little diagram and thought it was totally awesome and dorky, but when I looked at the preview it was all wonky. I tried to dewonkify it by bringing in the marks in the middle, but it's still pretty wonky.)
I envision that the difference in brightness between the two lights that is needed for there to only be one shadow is a rough equivalent to the extent of the difference in informational connectivity between the two systems at the point of their intersection for the one (in this case r-phase [eg. growth phase]) to overcode the other. I would then get readings with the object at different positions between the light sources to account for diffusion over distance.
The lights make sense to me because brightness and information are both considered logistically and they are in a sense variations on a theme. I just don't know at this point what those differences are in order to set parameters and I don't know at this point if this is an already-established relationship or not.
As far as the first point goes (relationship of dominance), a part of me sees it as an issue of the change in connection to the center multiplied by maximum connection to the center divided by the distance. There will be a log base (???) in there, either on the full expression or else just on the numerator, I'm not really sure. The log should probably be negative, too, since the rate of change will be negative and information entropy has a negative log. If this sounds like crap it very well could be since I last took calculus over 10 years ago and I was 18 and didn't care at all at the time.
As to why the approach I'm taking, in part it's due to the nature of the class and the discourse I'm somewhat trying to engage in. I'm doing all of this on STELLA at the moment, a fairly easy to work with GUI based modeling software. It's all stock and flow stuff, and although I know there are ways to incorporate stochastic parameters and other elements of probability into it, I don't actually know enough about those to have tried them yet. On the other hand, I know that this (or any) modeling approach is not sufficient for the full extent of what I'm looking at. At this point, though, I've developed a model of my two systems for themselves (one is simple exponential growth, the other incorporates resource depletion, increased extraction to make up for depletion, and feedbacks that limit that increase based on changing use and death rates). Now I need to figure out how to integrate them so the one can disturb the other in the hope that I can get a bifuraction or, better yet, get it to go chaotic to symbolize an approaching regime shift.
Ultimately, too, this will become a chapter in my thesis and eventual dissertation, for which I'm planning on writing a really awesome book (doesn't everyone...). The rest of my work will not be much in this direction (it's going to be all poststructural and crap), making for a fairly bipolar piece of work. I don't expect any of my code to be pretty (before this I haven't done any coding since my days playing with BASIC on an Apple IIe, although I recently got the Odum's modeling book and they use BASIC so there might be some life left in that language for me) - I'm just tooling with equations until I get the graph output I want. Justifications come later. My work is principally theory, I'm just using modeling as a means of creating justifications or quantifications for the larger issues I'm talking about. As far as any potential publications, Eco Complexity perhaps. I haven't though about it to that point yet. My thesis is the first target. After that it's just tweaking.
For those still reading this, I thought I should say a few words about the links I posted previously instead of simply posting them. James Kay was a theoretical ecologist that did really cool work incorporating the second law of thermodynamics (entropy) into an explanation of ecosystem development. Key papers are "Life as a Manifestation of the Second Law of Thermodynamics" and "Ecosystems as Self-organizing Holarchic Open Systems," both of which (and many more) are on his posthumous website. Robert Rosen was a theoretical biologist and complex systems theorist whose work might best be approached through his book _Essays on Life Itself_. The website has some of his work, and his daughter says she intends on posting all his work for free at some point. Resilience Alliance is a group of researchers on complex adaptive systems that is the current stomping grounds of CS (Buzz) Holling, an amazing ecologist who is largely responsible for the examination of resilience in systems and moving ecology away from a study of static systems. Lots of cool stuff.