We define chaotic motion for dynamical systems acting in finite, discrete spaces via the deterministic randomness of their trajectories. The theory of algorithmic complexity is used to provide the meaning of randomness for symbolic sequences derived from these trajectories, and a practical test of randomness is devised on the basis of an ideal, physically motivated, model of a computer. Two examples—a discretized standard map, and a fully connected neutral network—are studied analytically and numerically.
Applying Algorithmic Complexity to Define Chaos in the Motion of Complex Systems / Crisanti, Andrea; Falcioni, Massimo; G., Mantica; Vulpiani, Angelo. - In: PHYSICAL REVIEW E. - ISSN 1063-651X. - STAMPA. - 50:(1994), pp. 1959-1967. [10.1103/PhysRevE.50.1959]
Applying Algorithmic Complexity to Define Chaos in the Motion of Complex Systems
CRISANTI, Andrea;FALCIONI, Massimo;VULPIANI, Angelo
1994
Abstract
We define chaotic motion for dynamical systems acting in finite, discrete spaces via the deterministic randomness of their trajectories. The theory of algorithmic complexity is used to provide the meaning of randomness for symbolic sequences derived from these trajectories, and a practical test of randomness is devised on the basis of an ideal, physically motivated, model of a computer. Two examples—a discretized standard map, and a fully connected neutral network—are studied analytically and numerically.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
