arXiv subjects

M. G. Cosenza

Publications and source records attributed to M. G. Cosenza.

At least 55 records · Page 3Linked to original sources

arXiv2006

Intracultural diversity in a model of social dynamics

We study the consequences of introducing individual nonconformity in social interactions, based on Axelrod's model for the dissemination of culture. A constraint on the number of situations in which interaction may take place is introduced in order to lift the unavoidable ho mogeneity present in the final configurations arising in Axelrod's related models. The inclusion of this constraint leads to the occurrence of complex patterns of intracultural diversity whose statistical properties and spatial distribution are characterized by means of the concepts of cultural affinity and cultural cli ne. It is found that the relevant quantity that determines the properties of intracultural diversity is given by the fraction of cultural features that characterizes the cultural nonconformity of individuals.

nlin.AO↗

arXiv2006

Random global coupling induces synchronization and nontrivial collective behavior in networks of chaotic maps

The phenomena of synchronization and nontrivial collective behavior are studied in a model of coupled chaotic maps with random global coupling. The mean field of the system is coupled to a fraction of elements randomly chosen at any given time. It is shown that the reinjection of the mean field to a fraction of randomly selected elements can induce synchronization and nontrivial collective behavior in the system. The regions where these collective states emerge on the space of parameters of the system are calculated.

nlin.CD↗

arXiv2006

Phase ordering induced by defects in chaotic bistable media

The phase ordering dynamics of coupled chaotic bistable maps on lattices with defects is investigated. The statistical properties of the system are characterized by means of the average normalized size of spatial domains of equivalent spin variables that define the phases. It is found that spatial defects can induce the formation of domains in bistable spatiotemporal systems. The minimum distance between defects acts as parameter for a transition from a homogeneous state to a heterogeneous regime where two phases coexist The critical exponent of this transition also exhibits a transition when the coupling is increased, indicating the presence of a new class of domain where both phases coexist forming a chessboard pattern.

cond-mat.dis-nn↗

arXiv2006

Local versus global interactions in nonequilibrium transitions: A model of social dynamics

A nonequilibrium system of locally interacting elements in a lattice with an absorbing order-disorder phase transition is studied under the effect of additional interacting fields. These fields are shown to produce interesting effects in the collective behavior of this system. Both for autonomous and external fields, disorder grows in the system when the probability of the elements to interact with the field is increased. There exists a threshold value of this probability beyond which the system is always disordered. The domain of parameters of the ordered regime is larger for nonuniform local fields than for spatially uniform fields. However, the zero field limit is discontinous. In the limit of vanishingly small probability of interaction with the field, autonomous or external fields are able to order a system that would fall in a disordered phase under local interactions of the elements alone. We consider different types of fields which are interpreted as forms of mass media acting on a social system in the context of Axelrod's model for cultural dissemination.

cond-mat.stat-mech↗

arXiv2005

Nonequilibrium transition induced by mass media in a model for social influence

We study the effect of mass media, modeled as an applied external field, on a social system based on Axelrod's model for the dissemination of culture. The numerical simulations show that the system undergoes a nonequilibrium phase transition between an ordered phase (homogeneous culture) specified by the mass media and a disordered (culturally fragmented) one. The critical boundary separating these phases is calculated on the parameter space of the system, given by the intensity of the mass media influence and the number of options per cultural attribute. Counterintuitively, mass media can induce cultural diversity when its intensity is above some threshold value. The nature of the phase transition changes from continuous to discontinuous at some critical value of the number of options.

nlin.AO↗

arXiv2005

Synchronization and clustering in electroencephalographic signals

The degree of synchronization and the amount of dynamical cluster formation in electroencephalographic (EEG) signals are characterized by employing two order parameters introduced in the context of coupled chaotic systems subject to external noise. These parameters are calculated in EEG signals from a group of healthy subjects and a group of epileptic patients, including a patient experiencing an epileptic crisis. The evolution of these parameters shows the occurrence of intermittent synchronization and clustering in the brain activity during an epileptic crisis. Significantly, the existence of an instantaneous maximum of synchronization previous to the onset of a crisis is revealed by this procedure. The mean values of the order parameters and their standard deviations are compared between both groups of individuals.

nlin.CD↗

arXiv2005

Synchronization in driven versus autonomous coupled chaotic maps

The phenomenon of synchronization occurring in a locally coupled map lattice subject to an external drive is compared to the synchronization process in an autonomous coupled map system with similar local couplings plus a global interaction. It is shown that chaotic synchronized states in both systems are equivalent, but the collective states arising after the chaotic synchronized state becomes unstable can be different in these two systems. It is found that the external drive induces chaotic synchronization as well as synchronization of unstable periodic orbits of the local dynamics in the driven lattice. On the other hand, the addition of a global interaction in the autonomous system allows for chaotic synchronization that is not possible in a large coupled map system possessing only local couplings.

nlin.CD↗

arXiv2003

Spectral properties and pattern selection in fractal growth networks

A model for the generation of fractal growth networks in Euclidean spaces of arbitrary dimension is presented. These networks are considered as the spatial support of reaction-diffusion and pattern formation processes. The local dynamics at the nodes of a fractal growth network is given by a nonlinear map, giving raise to a coupled map system. The coupling is described by a matrix whose eigenvectors constitute a basis on which spatial patterns on fractal growth networks can be expressed by linear combination. The spectrum of eigenvalues the coupling matrix exhibits a nonuniform distribution that is reflected in the presence of gaps or niches in the boundaries of stability of the synchronized states on the space of parameters of the system. These gaps allow for the selection of specific spatial patterns by appropriately varying the parameters of the system.

nlin.PS↗

arXiv2003

Phase separation in coupled chaotic maps on fractal networks

The phase ordering dynamics of coupled chaotic maps on fractal networks are investigated. The statistical properties of the systems are characterized by means of the persistence probability of equivalent spin variables that define the phases. The persistence saturates and phase domains freeze for all values of the coupling parameter as a consequence of the fractal structure of the networks, in contrast to the phase transition behavior previously observed in regular Euclidean lattices. Several discontinuities and other features found in the saturation persistence curve as a function of the coupling are explained in terms of changes of stability of local phase configurations on the fractals.

nlin.CD↗

arXiv2002

Transition to Turbulence in Coupled Maps on Hierarchical Lattices

General hierarchical lattices of coupled maps are considered as dynamical systems. These models may describe many processes occurring in heterogeneous media with tree-like structures. The transition to turbulence via spatiotemporal intermittency is investigated for these geometries. Critical exponents associated to the onset of turbulence are calculated as functions of the parameters of the systems. No evidence of nontrivial collective behavior is observed in the global quantity used to characterize the spatiotemporal dynamics.

chao-dyn↗

arXiv2002

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.

nlin.CD↗

arXiv2002

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.

nlin.CD↗

arXiv2002

Coupled Map Networks as Communication Schemes

Networks of chaotic coupled maps are considered as string and language generators. It is shown that such networks can be used as encrypting systems where the ciphertext contains information about the evolution of the network and also about the way to select the plaintext symbols from the string associated to the network evolution. The secret key provides the network parameters, such as the coupling strengths.

nlin.CD↗

arXiv2001

Turbulence in small-world networks

The transition to turbulence via spatiotemporal intermittency is investigated in the context of coupled maps defined on small-world networks. The local dynamics is given by the Chaté-Manneville minimal map previously used in studies of spatiotemporal intermittency in ordered lattices. The critical boundary separating laminar and turbulent regimes is calculated on the parameter space of the system, given by the coupling strength and the rewiring probability of the network. Windows of relaminarization are present in some regions of the parameter space. New features arise in small-world networks; for instance, the character of the transition to turbulence changes from second order to a first order phase transition at some critical value of the rewiring probability. A linear relation characterizing the change in the order of the phase transition is found. The global quantity used as order parameter for the transition also exhibits nontrivial collective behavior for some values of the parameters. These models may describe several processes occurring in nonuniform media where the degree of disorder can be continuously varied through a parameter.

nlin.CD↗

arXiv2001

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.

nlin.CD↗

arXiv2001

Pattern Formation on Trees

Networks having the geometry and the connectivity of trees are considered as the spatial support of spatiotemporal dynamical processes. A tree is characterized by two parameters: its ramification and its depth. The local dynamics at the nodes of a tree is described by a nonlinear map, given rise to a coupled map lattice system. The coupling is expressed by a matrix whose eigenvectors constitute a basis on which spatial patterns on trees can be expressed by linear combination. The spectrum of eigenvalues of the coupling matrix exhibit a nonuniform distribution which manifest itself in the bifurcation structure of the spatially synchronized modes. These models may describe reaction-diffusion processes and several other phenomena occurring on heterogeneous media with hierarchical structure.

nlin.PS↗

arXiv1998

Cluster dynamics in systems with constant mean field coupling

A procedure to predict the occurrence of periodic clusters in a system of globally coupled maps displaying a constant mean field is presented. The method employs the analogy between a system of globally coupled maps and a single map driven by a constant force. By obtaining the asymptotic orbits of the driven map, an associated coupling function can be constructed. This function allows to establish a direct connection between both systems. Some applications are shown.

chao-dyn↗

arXiv1998

Driven Maps and the Emergence of Ordered Collective Behavior in Globally Coupled Maps

A method to predict the emergence of different kinds of ordered collective behaviors in systems of globally coupled chaotic maps is proposed. The method is based on the analogy between globally coupled maps and a map subjected to an external drive. A vector field which results from this analogy appears to govern the transient evolution of the globally coupled system. General forms of global couplings are considered. Some simple applications are given.

chao-dyn↗