Blog Post 4 - Experiment 1 Complete

I ended last week’s post with my findings regarding the inverse relationship between the chaos maximizing values of gain and spectral radius. Let’s see how this new information effects my experiment 1 results:

We finally have a positive Lyapunov exponent! However, the caveat is that the maximum Lyapunov exponent achieved is 0.025, which is barely chaotic. This might not necessarily be an issue, however. Recall my design of the network. I deliberately stated that I wanted my network to have biological constraints, such as Dale’s Law and an 80:20 E/I ratio. These rules effectively limit how chaotically my network behaves, so as long as my network has a positive Lyapunov exponent, I’m happy to continue. Furthermore, noise seems to have an upward effect on my Lyapunov exponent, which is understandable. Finally, for graph D, we can see that we really are sitting on the “edge of chaos,” where some trials diverge from one another while some stagnate and converge. I feel like I’ve found an alternate sweet spot for network behavior: I originally intended to have my network behave exclusively chaotically, but this might make results for my experiments even more interesting. I’ll be working on Experiment 2 next where the effects of the factors I discussed here will be put into play and shown.