What is the difference between Lyapunov Exponent vs time and Lyapunov Exponent vs parameter?
I noticed that some plot graph of Lyapunov Exponent but are not usually the same x-axis. Some plot graph Lyapunov vs time and and some plot Lyapunov vs parameter of the equation. But they do not specify the difference. What is the consensus on that. Furthermore, some refer to Lyapunov Exponent as Lyapunov number. The difference in graph is that the first can have negative values and other positive only. Why is that ? I know that
- Lya exp vs time tells me how long given parameters are stable before they go chaotic.
- Lya exp vs parameter tells me which parameter values contribute to chaos.
- Lya exp that has positive and negative values in axis tells me when it turn from stable to chaos.
- Lya number has only positive values but I do not know what information I can extract from that.