A model for cross-cultural reciprocal interactions through mass media

Local connectivity effects in learning and coordination dynamics in a two-layer network

Anticoordination and chimera states occur in a two-layer model of learning and coordination dynamics in fully connected networks. Learning occurs in the intra-layer networks, while a coordination game is played in the inter-layer network. In this paper, we study the robustness of these states against local effects introduced by the local connectivity of random networks. We identify threshold values for the mean degree of the networks such that below these values, local effects prevent the existence of anticoordination and chimera states found in the fully connected setting. Local effects in the intra-layer learning network are more important than in the inter-layer network in preventing the existence of anticoordination states. The local connectivity of the intra- and inter-layer networks is important to avoid the occurrence of chimera states, but the local effects are stronger in the inter-layer coordination network than in the intra-layer learning network. We also study the effect of local connectivity on the problem of equilibrium selection in the asymmetric coordination game, showing that local effects favor the selection of the Pareto-dominant equilibrium in situations in which the risk-dominant equilibrium is selected in the fully connected network. In this case, again, the important local effects are those associated with the coordination dynamics inter-layer network. Indeed, lower average degree of the network connectivity between layers reduces the probability of achieving the risk-dominant strategy, favoring the Pareto-dominant equilibrium.

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. We find situations where the largest minority group, possessing a cultural state different from that of the predominant trend transmitted by the mass media, can grow to almost half of the size of the population. We show that this phenomenon occurs when a critical number of long-range connections are present in the underlying network of interactions. We have numerically characterized four phases on the space of parameters of the system: an ordered phase; a semi-ordered phase where almost half of the population consists of the largest minority in a state different from that of the mass media; a disordered phase; and a chimera-like phase where one large domain coexists with many very small domains.

Influence of periodic external fields in multiagent models with language dynamics

We investigate large-scale effects induced by external fields, phenomenologically interpreted as mass media, in multiagent models evolving with the microscopic dynamics of the binary naming game. In particular, we show that a single external field, broadcasting information at regular time intervals, can reverse the majority opinion of the population, provided the frequency and the effectiveness of the sent messages lie above well-defined thresholds. We study the phase structure of the model in the mean field approximation and in numerical simulations with several network topologies. We also investigate the influence on the agent dynamics of two competing external fields, periodically broadcasting different messages. In finite regions of the parameter space we observe periodic equilibrium states in which the average opinion densities are reversed with respect to naive expectations. Such equilibria occur in two cases: (i) when the frequencies of the competing messages are different but close to each other; (ii) when the frequencies are equal and the relative time shift of the messages does not exceed half a period. We interpret the observed phenomena as a result of the interplay between the external fields and the internal dynamics of the agents and conclude that, depending on the model parameters, the naming game is consistent with scenarios of first- or second-mover advantage (to borrow an expression from the jargon of business strategy).

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. We use the normalized mutual information and the information transfer between global and local variables to characterize complete and generalized synchronization. We show that these information measures can characterize both types of synchronized states and also allow us to discern the origin of a global interaction field. A synchronization state emerges when a sufficient amount of information provided by a field is shared by all the elements in the system, on the average over long times. Thus, the maximum value of the top-down information transfer can be used as a predictor of synchronization in a system, as a parameter is varied.