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.
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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]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/244449
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