## 1998 |

Loreto, Vittorio; Serva, Maurizio; Vulpiani, Angelo On the concept of complexity of random dynamical systems (Journal Article) INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 12 (3) , pp. 225–243, 1998. (Abstract | Links | BibTeX | Tags: complexity, dynamical_systems, loreto) @article{b, title = {On the concept of complexity of random dynamical systems}, author = {Vittorio Loreto and Maurizio Serva and Angelo Vulpiani}, url = {http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.50.1146}, year = {1998}, date = {1998-01-01}, journal = {INTERNATIONAL JOURNAL OF MODERN PHYSICS B}, volume = {12 (3)}, pages = {225--243}, publisher = {WORLD SCIENTIFIC, SINGAPORE}, address = {Singapore}, abstract = {We show how to introduce a characterization the "complexity" of random dynamical systems. More precisely we propose a suitable indicator of complexity in terms of the average number of bits per time unit necessary to specify the sequence generated by these systems. This indicator of complexity, which can be extracted from real experimental data, turns out to be very natural in the context of information theory. For dynamical systems with random perturbations, it coincides with the rate K of divergence of nearby trajectories evolving under two different noise realizations. In presence of strong dynamical intermittency, the value of K is very different from the standard Lyapunov exponent chi(sigma) computed through the consideration of two nearby trajectories evolving under the same realization of the random perturbation. However, the former is much more relevant than the latter from a physical point of view as illustrated by some numerical examples of noisy and random maps.}, keywords = {complexity, dynamical_systems, loreto}, pubstate = {published}, tppubtype = {article} } We show how to introduce a characterization the "complexity" of random dynamical systems. More precisely we propose a suitable indicator of complexity in terms of the average number of bits per time unit necessary to specify the sequence generated by these systems. This indicator of complexity, which can be extracted from real experimental data, turns out to be very natural in the context of information theory. For dynamical systems with random perturbations, it coincides with the rate K of divergence of nearby trajectories evolving under two different noise realizations. In presence of strong dynamical intermittency, the value of K is very different from the standard Lyapunov exponent chi(sigma) computed through the consideration of two nearby trajectories evolving under the same realization of the random perturbation. However, the former is much more relevant than the latter from a physical point of view as illustrated by some numerical examples of noisy and random maps. |

## 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: complexity, dynamical_systems, loreto) @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://samarcanda.phys.uniroma1.it/vittorioloreto/PAPERS/1996/Loreto_PhysicaA_1996.pdf}, 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 = {complexity, dynamical_systems, loreto}, 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, statistical_physics) @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, statistical_physics}, 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. |

# Publications

adjacent possible air traffic complexity complex_networks complex_systems creativity cuskley data_compression dynamical_systems evolutionary_dynamics gravino information_theory innovation_dynamics kreyon language_dynamics language_games local optimization loreto modeling monechi opinion_dynamics phylogeny relevant_literature servedio social_dynamics statistical_physics techno_social_systems transportation networks tria zippers

## 1998 |

On the concept of complexity of random dynamical systems (Journal Article) INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 12 (3) , pp. 225–243, 1998. |

## 1996 |

Characterization of chaos in random maps (Journal Article) PHYSICA. A, 232 , pp. 189–200, 1996. |

Concept of complexity in random dynamical systems (Journal Article) PHYSICAL REVIEW E, 53 , pp. 2087–2098, 1996. |