Mass media competition and alternative ordering in social dynamics.

We investigate the collective behavior of a system of social agents subject to the competition between two mass media influences considered as external fields. We study under what conditions either of two mass media with different intensities can impose its message to the majority. In addition to a collective state dominated by the stronger mass media and a disordered phase, we characterize two nontrivial effects as the parameters of the system are varied: (i) the appearance of a majority sharing the state of the weaker mass media, and (ii) the emergence of an alternative ordering in a state different from those of either media.

Controlling systemic corruption through group size and salary dispersion of public servants.

We investigate an agent-based model for the emergence of corruption in public contracts. There are two types of agents: business people and public servants. Both business people and public servants can adopt two strategies: corrupt or honest behavior.

Coevolutionary Dynamics with Global Fields.

We investigate the effects of external and autonomous global interaction fields on an adaptive network of social agents with an opinion formation dynamics based on a simple imitation rule. We study the competition between global fields and adaptive rewiring on the space of parameters of the system. The model represents an adaptive society subject to global mass media such as a directed opinion influence or feedback of endogenous cultural trends.

Against mass media trends: Minority growth in cultural globalization.

We investigate the collective behavior of a globalized society under the influence of endogenous mass media trends. The mass media trend is a global field corresponding to the statistical mode of the states of the agents in the system. The interaction dynamics is based on Axelrod's rules for the dissemination of culture.

Asymmetric cluster and chimera dynamics in globally coupled systems.

We investigate the emergence of chimera and cluster states possessing asymmetric dynamics in globally coupled systems, where the trajectories of oscillators belonging to different subpopulations exhibit different dynamical properties. In an asymmetric chimera state, the trajectory of an element in the synchronized subset is stationary or periodic, while that of an oscillator in the desynchronized subset is chaotic. In an asymmetric cluster state, the periods of the trajectories of elements belonging to different clusters are different.

Chimeras and clusters in networks of hyperbolic chaotic oscillators.

We show that chimera states, where differentiated subsets of synchronized and desynchronized dynamical elements coexist, can emerge in networks of hyperbolic chaotic oscillators subject to global interactions. As local dynamics we employ Lozi maps, which possess hyperbolic chaotic attractors. We consider a globally coupled system of these maps and use two statistical quantities to describe its collective behavior: the average fraction of elements belonging to clusters and the average standard deviation of state variables.

Global interactions, information flow, and chaos synchronization.

We investigate the relationship between the emergence of chaos synchronization and the information flow in dynamical systems possessing homogeneous or heterogeneous global interactions whose origin can be external (driven systems) or internal (autonomous systems). By employing general models of coupled chaotic maps for such systems, we show that the presence of a homogeneous global field, either external or internal, for all times is not indispensable for achieving complete or generalized synchronization in a system of chaotic elements. Complete synchronization can also appear with heterogeneous global fields; it does not requires the simultaneous sharing of the field by all the elements in a system.

A model for cross-cultural reciprocal interactions through mass media.

We investigate the problem of cross-cultural interactions through mass media in a model where two populations of social agents, each with its own internal dynamics, get information about each other through reciprocal global interactions. As the agent dynamics, we employ Axelrod's model for social influence. The global interaction fields correspond to the statistical mode of the states of the agents and represent mass media messages on the cultural trend originating in each population.

Generalized synchronization of chaos in autonomous systems.

We extend the concept of generalized synchronization of chaos, a phenomenon that occurs in driven dynamical systems, to the context of autonomous spatiotemporal systems. It means a situation where the chaotic state variables in an autonomous system can be synchronized to each other, but not to a coupling function defined from them. The form of the coupling function is not crucial; it may not depend on all the state variables.

Phase growth in bistable systems with impurities.

A system of coupled chaotic bistable maps on a lattice with randomly distributed impurities is investigated as a model for studying the phenomenon of phase growth in nonuniform media. The statistical properties of the system are characterized by means of the average size of spatial domains of equivalent spin variables that define the phases. It is found that the rate at which phase domains grow becomes smaller when impurities are present and that the average size of the resulting domains in the inhomogeneous state of the system decreases when the density of impurities is increased.

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.

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.

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.

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.

Phase separation in coupled chaotic maps on fractal networks.

The phase ordering dynamics of coupled chaotic maps on fractal networks is 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.

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.

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 cipher text contains information about the evolution of the network and also about the way to select the plain text symbols from the string associated with the network evolution. The secret key provides the network parameters, such as the coupling strengths.

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 lattice. 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.

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.

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, giving rise to a coupled map lattice system.

Spatiotemporal intermittency on fractal lattices.

The transition to turbulence via spatiotemporal intermittency is investigated for coupled maps defined on generalized Sierpinski gaskets, a class of deterministic fractal lattices. Critical exponents that characterize the onset of intermittency are computed as a function of the fractal dimension of the lattice. Windows of spatiotemporal intermittency are found as the coupling parameter is varied for lattices with a fractal dimension greater than two.

Coupled maps and pattern formation on the Sierpinski gasket.

The bifurcation structure of coupled maps on the Sierpinski gasket is investigated. The fractal character of the underlying lattice gives rise to stability boundaries for the periodic synchronized states with unusual features and spatially inhomogeneous states with a complex structure. The results are illustrated by calculations on coupled quadratic and cubic maps.