I have these two models:
Both show Temperature vs Time for 15 different input conditions (i.e. inlet fuel velocity).
My question is: what is the difference between these two systems? Is one of them chaotic/non-chaotic? It is evident that the system on the left is independent of initial conditions as all values converge toward the end of the simulation - is that not the definition of non-chaotic dynamics? If so, since the other system "does care" about every change in the initial conditions - is it more chaotic?
Just trying to correctly formulate the difference in the underlying system dynamics.
I wouldn't describe either as chaotic. The second one does turn small differences into larger differences, but it does so in a very clear and predictable way.
For example, $a_0 \times 1.01^n$ also results in larger changes for small differences in the value of $a_0$, but in a nice and predictable way.
On the other hand, $x_{n+1} = kx_n(1-x_n)$ is very different, a small difference in the value of $k$ can result in wildly different behavior in the sequence of $x_n$.