Algorithmic Complexity Measure of the Dynamical Systems
Davoud Arasteh · ASME Press eBooks · 2006
Nonlinear systems can demonstrate various periodic as well as chaotic behaviors. To characterize their responses for the values of control parameters, different methods have been introduced. One of these methods is algorithmic complexity measure of the phase space attractors. We have applied this method to a discrete and a continuous dynamical system. Chaotic systems are deterministic constrained systems that are typically compressible compared to random systems. To quantify the order of organization, we have applied the algorithmic complexity theory to classify the order of organization in physical systems by studying their generated patterns and computing their degree of compressibility. We have shown that the order of organization for quasi-organized system is increasing logarithmically with the evolutionary length of the system. We believe that our approach addresses one of the most acknowledged features of quasi-organized system and quantitatively locates the quasi-organized systems between highly organized and constrained-unorganized (chaotic) systems.