## 1996 |

Loreto, Vittorio; Paladin, Giovanni; Pasquini, Michele; Vulpiani, Angelo Characterization of chaos in random maps Journal Article PHYSICA. A, 232 , pp. 189–200, 1996. Abstract | Links | BibTeX | Tags: dynamical_systems, loreto, paladin, pasquini, vulpiani @article{b, title = {Characterization of chaos in random maps}, author = {Vittorio Loreto and Giovanni Paladin and Michele Pasquini and Angelo Vulpiani}, url = {http://www.sciencedirect.com/science/article/pii/0378437196000878 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=A1996VN65900016&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=0c7ff228ccbaaa74236f48834a34396a}, year = {1996}, date = {1996-01-01}, journal = {PHYSICA. A}, volume = {232}, pages = {189--200}, publisher = {ELSEVIER SCIENCE, AMSTERDAM}, abstract = {We discuss the characterization of chaotic behaviors in random maps both in terms of the Lyapunov exponent and of the spectral properties of the Perron-Frobenius operator. In particular, we study a logistic map where the control parameter is extracted at random at each time step by considering finite-dimensional approximation of the Perron-Frobenius operator.}, keywords = {dynamical_systems, loreto, paladin, pasquini, vulpiani}, pubstate = {published}, tppubtype = {article} } We discuss the characterization of chaotic behaviors in random maps both in terms of the Lyapunov exponent and of the spectral properties of the Perron-Frobenius operator. In particular, we study a logistic map where the control parameter is extracted at random at each time step by considering finite-dimensional approximation of the Perron-Frobenius operator. |

Loreto, Vittorio; Paladin, Giovanni; Vulpiani, Angelo Concept of complexity in random dynamical systems Journal Article PHYSICAL REVIEW E, 53 , pp. 2087–2098, 1996. Abstract | Links | BibTeX | Tags: complexity, dynamical_systems, loreto, paladin, statistical_physics, vulpiani @article{b, title = {Concept of complexity in random dynamical systems}, author = {Vittorio Loreto and Giovanni Paladin and Angelo Vulpiani}, url = {http://pre.aps.org/abstract/PRE/v53/i3/p2087_1 http://samarcanda.phys.uniroma1.it/vittorioloreto/PAPERS/1996/Loreto_PhysRevE_1996.pdf}, year = {1996}, date = {1996-01-01}, journal = {PHYSICAL REVIEW E}, volume = {53}, pages = {2087--2098}, publisher = {AMERICAN PHYSICAL SOC}, abstract = {We introduce a measure of complexity in terms of the average number of bits per time unit necessary to specify the sequence generated by the system. In dynamical systems with small random perturbations, this indicator coincides with the rate K of divergence of nearby trajectories evolving under two different noise realizations. The meaning of K is discussed in the context of the information theory, and it is shown that it can be determined from real experimental data. In the presence of strong dynamical intermittency, the value of K is very different from the standard Lyapunov exponent lambda(sigma) computed considering two nearby trajectories evolving under the same realization of the randomness. However, the former is much more relevant than the latter from a physical point of view, as illustrated by some numerical computations for noisy maps and sandpile models.}, keywords = {complexity, dynamical_systems, loreto, paladin, statistical_physics, vulpiani}, pubstate = {published}, tppubtype = {article} } We introduce a measure of complexity in terms of the average number of bits per time unit necessary to specify the sequence generated by the system. In dynamical systems with small random perturbations, this indicator coincides with the rate K of divergence of nearby trajectories evolving under two different noise realizations. The meaning of K is discussed in the context of the information theory, and it is shown that it can be determined from real experimental data. In the presence of strong dynamical intermittency, the value of K is very different from the standard Lyapunov exponent lambda(sigma) computed considering two nearby trajectories evolving under the same realization of the randomness. However, the former is much more relevant than the latter from a physical point of view, as illustrated by some numerical computations for noisy maps and sandpile models. |

Caglioti, Emanuele; Loreto, Vittorio Dynamical properties and predictability in a class of self-organized critical models Journal Article PHYSICAL REVIEW E, 53 , pp. R2953–R2956, 1996. Abstract | Links | BibTeX | Tags: caglioti, dynamical_systems, loreto, self_organization, statistical_physics @article{b, title = {Dynamical properties and predictability in a class of self-organized critical models}, author = {Emanuele Caglioti and Vittorio Loreto}, url = {http://pre.aps.org/abstract/PRE/v53/i3/p2953_1 http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=A1996UA37100116&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=0c7ff228ccbaaa74236f48834a34396a}, year = {1996}, date = {1996-01-01}, journal = {PHYSICAL REVIEW E}, volume = {53}, pages = {R2953--R2956}, publisher = {AMERICAN PHYSICAL SOC}, abstract = {We consider a particular class of self-organized critical models. For these systems we show that the Lyapunov exponent is strictly lower than zero. That allows us to describe the dynamics in terms of a piecewise linear contractive map. We describe the physical mechanisms underlying the approach to the recurrent set in the configuration space and we discuss the structure of the attractor for the dynamics. Finally the problem of the chaoticity of these systems and the definition of a predictability are addressed.}, keywords = {caglioti, dynamical_systems, loreto, self_organization, statistical_physics}, pubstate = {published}, tppubtype = {article} } We consider a particular class of self-organized critical models. For these systems we show that the Lyapunov exponent is strictly lower than zero. That allows us to describe the dynamics in terms of a piecewise linear contractive map. We describe the physical mechanisms underlying the approach to the recurrent set in the configuration space and we discuss the structure of the attractor for the dynamics. Finally the problem of the chaoticity of these systems and the definition of a predictability are addressed. |

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