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Equations governing the nonlinear dynamics of complex systems are usuallyunknown and indirect methods are used to reconstruct their manifolds. In turn,they depend on embedding parameters requiring other methods and long temporalsequences to be accurate. In this paper, we show that an optimal reconstructioncan be achieved by lossless compression of system's time course, providing aself-consistent analysis of its dynamics and a measure of its complexity, evenfor short sequences. Our measure of complexity detects system's state changessuch as weak synchronization phenomena, characterizing many systems, in onestep, integrating results from Lyapunov and fractal analysis.

Compressing phase space detects state changes in nonlinear dynamical systems