Many real-world networks are characterized by adaptive changes in their topology depending on the state of their nodes. Here we study epidemic dynamics on an adaptive network, where the susceptibles are able to avoid contact with the infected by rewiring their network connections. This gives rise to assortative degree correlation, oscillations, hysteresis, and first order transitions. We propose a low-dimensional model to describe the system and present a full local bifurcation analysis. Our results indicate that the interplay between dynamics and topology can have important consequences for the spreading of infectious diseases and related applications. DOI: 10.1103/PhysRevLett.96.208701 PACS numbers: 89.75.Hc, 87.19.Xx, 89.75.Fb In the physical literature the dynamics of complex networks has recently received much attention, with many applications in social, biological, and technical systems [1,2]. In particular, most research has been directed in two distinct directions. On the one hand, attention has been paid to the structure of the networks, revealing that simple dynamical rules, such as preferential attachment or selective rewiring, can be used to generate complex topologies [3][4][5][6]. Many of these rules are not only a useful tool for the generation of model graphs, but are also believed to shape real-world networks like the internet or the network of social contacts. On the other hand, research has focused on large ensembles of dynamical systems, where the interaction between individual units is described by a complex graph [7][8][9][10][11][12][13][14][15]. These studies have shown that the network topology can have a strong impact on the dynamics of the nodes, e.g., the absence of epidemic thresholds on scale free networks [7,8] or the detrimental effect of assortative degree correlations on targeted vaccination [12]. In the past the cross fertilization between these two lines of thought has led to considerable advances. However, the dynamics of networks and the dynamics on networks are still generally studied separately. In doing so, a characteristic features of many real-world networks is not taken into account, namely, the ability to adapt the network topology dynamically in response to the dynamic state of nodes [16 -19].Consider, for example, the spreading of an infectious disease on a social network. Humans tend to respond to the emergence of an epidemic by avoiding contacts with infected individuals. Such rewiring of the local connections can have a strong effect on the dynamics of the disease, which in turn influences the rewiring process. Thus, a complicated mutual interaction between a time varying network topology and the dynamics of the nodes emerges.In this Letter we study a susceptible-infectedsusceptible (SIS) model on an adaptive network. We demonstrate that a simple intuitive rewiring rule for the network connections has a profound impact on the emerging network, and is able to generate specific network properties such as a wide degree distribution, assortative degree correlatio...

Adaptive networks appear in many biological applications. They combine topological evolution of the network with dynamics in the network nodes. Recently, the dynamics of adaptive networks has been investigated in a number of parallel studies from different fields, ranging from genomics to game theory. Here we review these recent developments and show that they can be viewed from a unique angle. We demonstrate that all these studies are characterized by common themes, most prominently: complex dynamics and robust topological self-organization based on simple local rules.

Conflicting interests among group members are common when making collective decisions, yet failure to achieve consensus can be costly. Under these circumstances individuals may be susceptible to manipulation by a strongly opinionated, or extremist, minority. It has previously been argued, for humans and animals, that social groups containing individuals who are uninformed, or exhibit weak preferences, are particularly vulnerable to such manipulative agents. Here, we use theory and experiment to demonstrate that, for a wide range of conditions, a strongly opinionated minority can dictate group choice, but the presence of uninformed individuals spontaneously inhibits this process, returning control to the numerical majority. Our results emphasize the role of uninformed individuals in achieving democratic consensus amid internal group conflict and informational constraints. S ocial organisms must often achieve a consensus to obtain the benefits of group living and to avoid the costs of indecision (1 12). In some societies, notably those of eu social insects, making consensus decisions is often a unitary, conflict free process because the close relatedness among individuals means that they typically share preferences (11). However, in other social animals, such as schooling fub, flocking birds, herding ungulates, and humans, individual groop members may be oflow relatedness; thus, self interest can play an important role in group decisions. Reaching a consensus decision, there fore, frequently depends on individuals resolving complex conilicts of interest (1 11, 13, 14).There are several means of achieving groop consensus. In some cases, decisions made by one or only a small proportion of the group dictate the behavior of the entire group ( 4 6, 13, 14). There fore, a minority, or even a single individual, has the potential to control or exploit the majority, achieving substantial gains at the expense of other group members (1 6,9,10,14). In contrast, consensus can also be reached throogh demo cratic means, with fuir representation and an out come determined by a plurality. Democratic decisions tend to be more moderate, rninimiz ing group consensus costs, particularly in large animal groops (3). However, in the absence of established procedures such as voting ( 8), it is IDlclear how equal representation is enforced Consequently, for both human socwtJes (1,2,6,9,10,14) and group living animals ( 6, 13), it has been afb'lted that group decisions can be subject to manipulation by a self interested and opinionated minority. In particular, previoos work suggests that groups containing individu als who are uninformed, or naive, about the de cision being made are particularly vulnerable to such manipulation (2,9,10,13). Under this view, IDlinformed individuals destabilize the capacity for collective intelligence in groups (J 0, 14), with poorly informed individuals potentially facilitat ing the establishment of extremist opinions in populations (9,14).Here, we address the question of whether and, if so, under which condit...

The neural criticality hypothesis states that the brain may be poised in a critical state at a boundary between different types of dynamics. Theoretical and experimental studies show that critical systems often exhibit optimal computational properties, suggesting the possibility that criticality has been evolutionarily selected as a useful trait for our nervous system. Evidence for criticality has been found in cell cultures, brain slices, and anesthetized animals. Yet, inconsistent results were reported for recordings in awake animals and humans, and current results point to open questions about the exact nature and mechanism of criticality, as well as its functional role. Therefore, the criticality hypothesis has remained a controversial proposition. Here, we provide an account of the mathematical and physical foundations of criticality. In the light of this conceptual framework, we then review and discuss recent experimental studies with the aim of identifying important next steps to be taken and connections to other fields that should be explored.