Measuring dependency of chaotic systems on initial values by Lyapunov exponent, an original trajectory along with a perturbed one is needed, but I cannot understand the connection with the following article, (fig.3 of the article).
Masoud Abbaszadeh
It's a measure of sensitivity of the trajectory to the initial condition perturbations. If Lyapunov exponent is negative the two trajectories resulted from two different initial conditions, exponentially merge in time. It can also be seen as a measure of stiffness of the underlying ODE.
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