It is clear that a dynamic system might exhibit chaotic behavior (complexity), if internal feedback loops (nonlinear dynamics) exist among its interacting components for a certain range of control parameter values and the system is far from thermodynamic equilibrium (e.g. oscillating reactions). My question is: Is there a systematic methodology (algorithm) to find the ranges of values for which the system exhibits chaos?
Yes-by computing, for example, the greatest Lyapunov exponent and checking that it saturates.
One of the ways is to calculate the largest Lyapunov exponent. For example see
http://sprott.physics.wisc.edu/chaos/lyapexp.htm
But it is of course possible to calculate the Lyapunov spectrum.
Article Determining Lyapunov Exponents From a Time Series
I agree with previous answers. Lyapunov exponent is maybe the best option.
For these purposes bifurcation diagrams are often used.
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