# Adaptive Coevolutionary Networks

**Adaptive networks** (also called **coevolutionary networks**) are a class of dynamical and dynamically evolving networks. The defining feature of adaptive networks is the presence of a feedback loop between a dynamical process taking place on the network and a dynamically evolvig network structure. The interplay between these two types of dynamics can lead to a rich interplay that is thought to drive the dynamics and development of many real world networks.

Every network is a system of discrete *nodes* connected by *links*. Applied to such systems the word *dynamic* can have two different meanings. First, a network can be dynamic because the network *topology* (the specific structure of nodes and links) evolves in time. In this sense, for instance every growing network such as the Barabasi-Albert Model is dynamic. Second, a network can be dynamic because there is a dynamical process taking place on the network. Well-studied examples include for instance models of disease spreading or opinion formation on static networks. We can thus distinguish between the *dynamics of networks* and *dynamic on networks*. Adaptive networks combine these two types of dynamics. In particular one talks of adaptive networks when the dynamics of and on the networks interact.
Such an interplay is found in a wide range of real world systems and gives rise to a range of phenomena that are not observed either dynamics on networks or dynamics of networks in isolation.

## Contents |

## Historical Development

## Adaptive Interplay

## Application Areas

### Neural Criticality

### Opinion Formation

### Syncronization

### Epidemics

### Cooperation

### Other Applications

## Theoretical Tools

### Homogeneous Approxiamtion Schemes

### Heterogeneous Approximation Schemes

### Active Linking

### Other Approaches

## References

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