Model of Neuronal Network

Each of N boolean elements has K inputs and 0..N-1 outputs. Initial values and inputs are assigned randomly. At every time step "average input" [math]\bar{in}=\frac{1}{K}\sum_{all \ inputs}^{}{input}[/math] is calculated. In non-linear case it transforms to [math]\bar{in} \to -4 \bar{in}(\bar{in}-1)[/math] New value of element calculates depending on lim1 and lim2 parameters: If [math]\bar{in}[/math] > lim2 OR [math]\bar{in}[/math] < lim1 then res = 0 else res = 1

Net with N elements has [math]2^N[/math] distinct states. So any state sooner or later will be repeated, forming a loop with length L. But if L ~ [math]2^N[/math], timeline looks like set of random points - it is [i]determenistic chaos[/i]; Also we can discover[i] flip-flop loops[/i] with L ~ 1..5 and [i]long-period patterns[/i]. Loop with L=1 is stable and in this case animation stops. Try to find out, how these kinds of behavior depend of parameters lim1, lim2 and K!