Turbulence in Globally Coupled Maps

The phenomenon of turbulence is investigated in the context of globally coupled maps. The local dynamics is given by the Chat\'e-Manneville minimal map previously used in studies of spatiotemporal intermittency in locally coupled map lattices. New features arise in the globally coupled system; for instance, the transition to turbulence takes place discontinuously at some critical values of the parameters of the system. The critical boundaries between different regimes (laminar, turbulent and fully turbulent) of the system are calculated on the parameter space. Windows of turbulence are present on some ranges of the coupling parameter. The system also exhibits nontrivial collective behavior. A map for the instantaneous fraction of turbulent elements is proposed. This map describes many of the observed properties of the system.Comment: 6 pages LaTeX; 6 figures available upon request from authors. To appear in Phys. Rev. E (1996

Information transfer and nontrivial collective behavior in chaotic coupled map networks

The emergence of nontrivial collective behavior in networks of coupled chaotic maps is investigated by means of a nonlinear mutual prediction method. The resulting prediction error is used to measure the amount of information that a local unit possesses about the collective dynamics. Applications to locally and globally coupled map systems are considered. The prediction error exhibits phase transitions at critical values of the coupling for the onset of ordered collective behavior in these networks. This information measure may be used as an order parameter for the characterization of complex behavior in extended chaotic systems.Comment: 4 pp.,4 figs., Accepted in Phys. Rev. E, Rapid Communications (2002

Hierarchical Model for the Evolution of Cloud Complexes

The structure of cloud complexes appears to be well described by a "tree structure" representation when the image is partitioned into "clouds". In this representation, the parent-child relationships are assigned according to containment. Based on this picture, a hierarchical model for the evolution of Cloud Complexes, including star formation, is constructed, that follows the mass evolution of each sub-structure by computing its mass exchange (evaporation or condensation) with its parent and children, which depends on the radiation density at the interphase. For the set of parameters used as a reference model, the system produces IMFs with a maximum at too high mass (~2 M_sun) and the characteristic times for evolution seem too long. We show that these properties can be improved by adjusting model parameters. However, the emphasis here is to illustrate some general properties of this nonlinear model for the star formation process. Notwithstanding the simplifications involved, the model reveals an essential feature that will likely remain if additional physical processes are included. That is: the detailed behavior of the system is very sensitive to variations on the initial and external conditions, suggesting that a "universal" IMF is very unlikely. When an ensemble of IMFs corresponding to a variety of initial or external conditions is examined, the slope of the IMF at high masses shows variations comparable to the range derived from observational data. (Abridged)Comment: Latex, 29 pages, 13 figures, accepted for publication in Ap

Bounded Confidence under Preferential Flip: A Coupled Dynamics of Structural Balance and Opinions

In this work we study the coupled dynamics of social balance and opinion formation. We propose a model where agents form opinions under bounded confidence, but only considering the opinions of their friends. The signs of social ties -friendships and enmities- evolve seeking for social balance, taking into account how similar agents' opinions are. We consider both the case where opinions have one and two dimensions. We find that our dynamics produces the segregation of agents into two cliques, with the opinions of agents in one clique differing from those in the other. Depending on the level of bounded confidence, the dynamics can produce either consensus of opinions within each clique or the coexistence of several opinion clusters in a clique. For the uni-dimensional case, the opinions in one clique are all below the opinions in the other clique, hence defining a "left clique" and a "right clique". In the two-dimensional case, our numerical results suggest that the two cliques are separated by a hyperplane in the opinion space. We also show that the phenomenon of unidimensional opinions identified by DeMarzo, Vayanos and Zwiebel (Q J Econ 2003) extends partially to our dynamics. Finally, in the context of politics, we comment about the possible relation of our results to the fragmentation of an ideology and the emergence of new political parties.Comment: 8 figures, PLoS ONE 11(10): e0164323, 201

Field evidence of social influence in the expression of political preferences: the case of secessionist flags in Barcelona

Different models of social influence have explored the dynamics of social contagion, imitation, and diffusion of different types of traits, opinions, and conducts. However, few behavioral data indicating social influence dynamics have been obtained from direct observation in `natural' social contexts. The present research provides that kind of evidence in the case of the public expression of political preferences in the city of Barcelona, where thousands of citizens supporting the secession of Catalonia from Spain have placed a Catalan flag in their balconies. We present two different studies. 1) In July 2013 we registered the number of flags in 26% of the the city. We find that there is a large dispersion in the density of flags in districts with similar density of pro-independence voters. However, we find that the density of flags tends to be fostered in those electoral district where there is a clear majority of pro-independence vote, while it is inhibited in the opposite cases. 2) During 17 days around Catalonia's 2013 National Holiday we observed the position at balcony resolution of the flags displayed in the facades of 82 blocks. We compare the clustering of flags on the facades observed each day to equivalent random distributions and find that successive hangings of flags are not independent events but that a local influence mechanism is favoring their clustering. We also find that except for the National Holiday day the density of flags tends to be fostered in those facades where there is a clear majority of pro-independence vote.Comment: 27 pages, 13 figures, 2 table

Dynamics of Coupling Functions in Globally Coupled Maps: Size, Periodicity and Stability of Clusters

It is shown how different globally coupled map systems can be analyzed under a common framework by focusing on the dynamics of their respective global coupling functions. We investigate how the functional form of the coupling determines the formation of clusters in a globally coupled map system and the resulting periodicity of the global interaction. The allowed distributions of elements among periodic clusters is also found to depend on the functional form of the coupling. Through the analogy between globally coupled maps and a single driven map, the clustering behavior of the former systems can be characterized. By using this analogy, the dynamics of periodic clusters in systems displaying a constant global coupling are predicted; and for a particular family of coupling functions, it is shown that the stability condition of these clustered states can straightforwardly be derived.Comment: 12 pp, 5 figs, to appear in PR

On the Thermal Instability in a Contracting Gas Cloud and Formation of a Bound Cluster

We perform linear analysis of thermal instability in a contracting large cloud filled with warm HI gas and investigate the effect of metallicity and radiation flux. When the cloud reaches critical density n_f, the cloud fragments into cool, dense condensations because of thermal instability. For a lower metallicity gas cloud, the value of n_f is high. Collision between condensations will produce self-gravitating clumps and stars thereafter. From the result of calculation, we suggest that high star formation efficiency and bound cluster formation are realized in low-metallicity and/or strong-radiation environments.Comment: 7 pages, including 7 figures, LaTeX2e(emulateapj5.sty) To appear in ApJ, Jun 10, 200

Simple Models for Turbulent Self-Regulation in Galaxy Disks

We propose that turbulent heating, wave pressure and gas exchanges between different regions of disks play a dominant role in determining the preferred, quasi-equilibrium, self-similar states of gas disks on large-scales. We present simple families of analytic, thermohydrodynamic models for these global states, which include terms for turbulent pressure and Reynolds stresses. Star formation rates, phase balances, and hydrodynamic forces are all tightly coupled and balanced. The models have stratified radial flows, with the cold gas slowly flowing inward in the midplane of the disk, and with the warm/hot phases that surround the midplane flowing outward. The models suggest a number of results that are in accord with observation, as well as some novel predictions, including the following. 1) The large-scale gas density and thermal phase distributions in galaxy disks can be explained as the result of turbulent heating and spatial couplings. 2) The turbulent pressures and stresses that drive radial outflows in the warm gas also allow a reduced circular velocity there. This effect was observed by Swaters, Sancisi and van der Hulst in NGC 891, a particularly turbulent edge-on disk. The models predict that the effect should be universal in such disks. 3) They suggest that a star formation rate like the phenomenological Schmidt Law is the natural result of global thermohydrodynamical balance, and may not obtain in disks far from equilibrium. (Abridged)Comment: 37 pages, 1 gif figure, accepted for publication in the Astrophysical Journa

Emergence of patterns in driven and in autonomous spatiotemporal systems

The relationship between a driven extended system and an autonomous spatiotemporal system is investigated in the context of coupled map lattice models. Specifically, a locally coupled map lattice subjected to an external drive is compared to a coupled map system with similar local couplings plus a global interaction. It is shown that, under some conditions, the emergent patterns in both systems are analogous. Based on the knowledge of the dynamical responses of the driven lattice, we present a method that allows the prediction of parameter values for the emergence of ordered spatiotemporal patterns in a class of coupled map systems having local coupling and general forms of global interactions.Comment: 7 pages, 3 figs, submitted to PRE (2002