No abstract

We explore the coupled dynamics of the internal states of a set of interacting elements and the network of interactions among them. Interactions are modeled by a spatial game and the network of interaction links evolves adapting to the outcome of the game. As an example we consider a model of cooperation, where the adaptation is shown to facilitate the formation of a hierarchical interaction network that sustains a highly cooperative stationary state. The resulting network has the characteristics of a small world network when a mechanism of local neighbor selection is introduced in the adaptive network dynamics. The highly connected nodes in the hierarchical structure of the network play a leading role in the stability of the network. Perturbations acting on the state of these special nodes trigger global avalanches leading to complete network reorganization.

We study a coevolution voter model on a complex network. A mean-field approximation reveals an absorbing transition from an active to a frozen phase at a critical value p c ÿ2 ÿ1 that only depends on the average degree of the network. In finite-size systems, the active and frozen phases correspond to a connected and a fragmented network, respectively. The transition can be seen as the sudden change in the trajectory of an equivalent random walk at the critical point, resulting in an approach to the final frozen state whose time scale diverges as jp c ÿ pj ÿ1 near p c . DOI: 10.1103/PhysRevLett.100.108702 PACS numbers: 89.75.Fb, 05.40.ÿa, 05.65.+b, 89.75.Hc The dynamics of collective phenomena in a system of interacting units depends on both the topology of the network of interactions and the interaction rule among connected units. The effects of these two ingredients on the emergent phenomena in a fixed network have been extensively studied. However, in many instances, both the structure of the network and the dynamical processes on it evolve in a coupled manner [1,2]. In particular, in the dynamics of social systems (Refs. [1,[3][4][5] and references therein), the network of interactions is not an exogenous structure, but it evolves and adapts driven by the changes in the state of the nodes that form the network. In recent models implementing this type of coevolution dynamics [2,4 -12] a transition is often observed from a phase where all nodes are in the same state forming a single connected network to a phase where the network is fragmented into disconnected components, each composed by nodes in the same state [13].In this Letter we address the question of how generic this type of transition is and the mechanism behind it. For this purpose, we introduce a minimal model of interacting binary state nodes that incorporates two basic features shared by many models displaying a fragmentation transition: (i) two or more absorbing states in a fixed connected network, and (ii) a rewiring rule that does not increase the number of links between nodes in the opposite state. The state dynamics consists of nodes copying the state of a random neighbor, while the network dynamics results from nodes dropping their links with opposite-state neighbors and creating new links with randomly selected same-state nodes. This model can be thought of as a coevolution version of the voter model [14] in which agents may select their interacting partners according to their states. It has the advantage of being analytically tractable and allows a fundamental understanding of the network fragmentation, explaining the transition numerically observed in related models [5,[8][9][10][11][12]. The mechanism responsible for the transition is the competition between two internal time scales, happening at a critical value that controls the relative ratio of these scales.We consider a network with N nodes. Initially, each node is endowed with a state 1 or ÿ1 with the same probability 1=2, and it is randomly connected to exactly neighbors, formi...

Polarization-state selection, polarization-state dynamics, and polarization switching of a quantum-well verticalcavity surface-emitting laser (VCSEL) for the lowest order transverse spatial mode of the laser is explored using a recently developed model that incorporates material birefringence, the saturable dispersion characteristic of semiconductor physics, and the sensitivity of the transitions in the material to the vector character of the electric field amplitude. Three features contribute to the observed linearly polarized states of emission: linear birefringence, linear gain or loss anisotropies, and an intermediate relaxation rate for imbalances in the populations of the magnetic sublevels. In the absence of either birefringence or saturable dispersion, the gain or loss anisotropies dictate stability for the linearly polarized mode with higher net gain; hence, switching is only possible if the relative strength of the net gain for the two modes is reversed. When birefringence and saturable dispersion are both present, there are possibilities of bistability, monostrability, and dynamical instability, including switching by destabilization of the mode with the higher gain to loss ratio in favor of the weaker mode. We compare our analytical and numerical results with recent experimental results on bistability and switchings caused by changes in the injection current and changes in the intensity of an injected optical signal.

Studies of cultural differentiation have shown that social mechanisms that normally lead to cultural convergence-homophily and influence-can also explain how distinct cultural groups can form. However, this emergent cultural diversity has proven to be unstable in the face of cultural drift-small errors or innovations that allow cultures to change from within. The authors develop a model of cultural differentiation that combines the traditional mechanisms of homophily and influence with a third mechanism of network homophily, in which network structure co-evolves with cultural interaction. Results show that in certain regions of the parameter space, these co-evolutionary dynamics can lead to patterns of cultural diversity that are stable in the presence of cultural drift. The authors address the implications of these findings for understanding the stability of cultural diversity in the face of increasing technological trends toward globalization.

We analyze the nonequilibrium order-disorder transition of Axelrod's model of social interaction in several complex networks. In a small-world network, we find a transition between an ordered homogeneous state and a disordered state. The transition point is shifted by the degree of spatial disorder of the underlying network, the network disorder favoring ordered configurations. In random scale-free networks the transition is only observed for finite size systems, showing system size scaling, while in the thermodynamic limit only ordered configurations are always obtained. Thus, in the thermodynamic limit the transition disappears. However, in structured scale-free networks, the phase transition between an ordered and a disordered phase is restored.

No abstract

We analyze the ordering dynamics of the voter model in different classes of complex networks. We observe that whether the voter dynamics orders the system depends on the effective dimensionality of the interaction networks. We also find that when there is no ordering in the system, the average survival time of metastable states in finite networks decreases with network disorder and degree heterogeneity. The existence of hubs in the network modifies the linear system size scaling law of the survival time. The size of an ordered domain is sensitive to the network disorder and the average connectivity, decreasing with both; however it seems not to depend on network size and degree heterogeneity.