The following is a follow-up to my transfer function post a couple of days ago. Two persons have suggested using a simpler non-monotonic function such as the Gaussian. I will incorporate results with that transfer function. Also, I will add one more category to my previous minimalistic categorizationof asymptotic dynamics: point attractors versus other dynamics. I am now including periodic orbits. Still very minimalistic.
Each point in the data bellow corresponds to generating 1000 CTRNNs and estimating whether the dynamics after 100 units of time (with 0.01 time-step) are: (1) point attractor (black), (2) periodic stable orbit (gray), or (3) something else (white).
CTRNNs are drawn at random from the same parameters as before, except that I have made the range of time-constants a bit smaller (to lessen the possibility of transients after 100 units of time) to [e^0,e^3]. Also changed the initial state of the activations of all neurons to randomly between [-10,10].
Experiments were run with circuits of size 2 to 20, and with three transfer functions: logistic, Gaussian, and tanh+sin. In the case of the Gaussian transfer function, the mean is always 0 while the standard deviation for each node is a random number between [1,3]. In the case of the f=a*tanh() + (1-a)sin() function a is a random number in [0,1] for each node in the circuit.
I will give some analysis later, I have to do a bunch of other stuff today first… sorry.