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.

We propose a model for studying binary fluids based on the mesoscopic molecular simulation technique known as multiparticle collision, where the space and state variables are continuous, and time is discrete. We include a repulsion rule to simulate segregation processes that does not require calculation of the interaction forces between particles, so binary fluids can be described on a mesoscopic scale. The model is conceptually simple and computationally efficient; it maintains Galilean invariance and conserves the mass and energy in the system at the micro- and macro-scale, whereas momentum is conserved globally. For a wide range of temperatures and densities, the model yields results in good agreement with the known properties of binary fluids, such as the density profile, interface width, phase separation, and phase growth. We also apply the model to the study of binary fluids in crowded environments with consistent results.

We investigate the synchronization behavior and the emergence of chimera states in a system of two interacting populations of maps possessing chaotic neural-like dynamics. We characterize four collective states on the space of coupling parameters of the system: complete synchronization, generalized synchronization, chimera states, and incoherence. We quantify the information exchange between the two neuron populations in chimera states. We have found a well-defined direction of the flow of information in chimera states, from the desynchronized population to the synchronized one. The incoherent population functions as a driver of the coherent neuron population in a chimera state. This feature is independent of the population sizes or population partitions. Our results yield insight into the communication mechanisms arising in brain processes such as unihemispheric sleep and epileptic seizures that have been associated to chimera states.

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.Comment: 4 pp, 4 ps figs, 1 ps tabl

We show that dynamical clustering, where a system segregates into distinguishable subsets of synchronized elements, and chimera states, where differentiated subsets of synchronized and desynchronized elements coexist, can emerge in networks of globally coupled robust‐chaos oscillators. We describe the collective behavior of a model of globally coupled robust‐chaos maps in terms of statistical quantities and characterize clusters, chimera states, synchronization, and incoherence on the space of parameters of the system. We employ the analogy between the local dynamics of a system of globally coupled maps with the response dynamics of a single driven map. We interpret the occurrence of clusters and chimeras in a globally coupled system of robust‐chaos maps in terms of windows of periodicity and multistability induced by a drive on the local robust‐chaos map. Our results show that robust‐chaos dynamics does not limit the formation of cluster and chimera states in networks of coupled systems, as it had been previously conjectured.

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. We show that, in both situations, global mass media contribute to consensus and to prevent the fragmentation of the social network induced by the coevolutionary dynamics. We present a discussion of these results in the context of dynamical systems and opinion formation dynamics.