It's Day 3 of BioQUEST. They always keep you busy for the first couple of days doing a mini-project, which breaks the ice and helps to get you situated with the available tools and resources. I recruited a couple of folks to work with me on a project idea I came up with. This year's session is about system biology and modelling. All of the tools they introduced, however, were based on deterministic modelling, rather than stochastic modelling. I thought it would be interesting to come up with an example of a stochastic and deterministic model and try to demonstrate how you could use a stochastic model in a form that was more accessible to students and use it to bridge the concepts and get students to begin exploring the deterministic model with more confidence. We tried a couple of different kinetics models, but ended up using the logistic growth equation. We adapted a Netlogo simple birth rate model for the stochastic model and built a deterministic model in JSim. I was hoping to demonstrate how with different values of "r", the logistic growth equation becomes unrealistic and demonstrates monotonic damping, periodic oscillation, and chaotic oscillation, but it turns out it only does that when you use the "discrete" solution of the formula. When you use the continuous form (integrating the differental equation), it stays nice and smooth and we couldn't figure out how to do a discrete solution using JSim. So we built a discrete version using a spreadsheet (I won't say which one.) Here's what it looks like with r=1.97.

monotonic.jpg

I learned quite a bit about using JSim and trying to work with differential equations. I also realised that the issue reminded me of the issues that Wolfram raises in A New Kind of Science. I haven't read the whole book yet, but I've read some of the preface, and it appears to me that he's saying that computational models that operate at the level of entitities in a complex system can produce better results than trying to describe the system mathematically. In any event, wwe got many positive comments on our poster and I was very pleased with the outcome. Now we have a little breathing space until we begin working on projects for the rest of the week.


StevenBrewer