Dynamics of complex systems consisted of many interacting active elements have recently attracted much attention when studying collective phenomena in natural and social sciences.The resulting behavior of such networked systems is based on the interplay between the individual dynamics of the elements(nodes),the evolution of the links between them,and the dynamics of the topology,i.e.,the specific pattern of nodes and links.Neuronal networks are of particular interest in this context since they are usually characterized by nontrivial intrinsic dynamics of nodes(neurons)and links(synaptic couplings)and rather complicated structure with adaptive properties.Many neurobiological experiments indicate that some important neural functions(e.g.,coding of sensory inputs)are performed due to switching between different collective states of the network [1].From the viewpoint of dynamical systems theory,such behavior cannot be described in terms of attractors in phase space because all meaningful events occur during transient dynamics towards some final attractor.Recently,some models have been proposed to describe sequential dynamics of transitions between metastable states [2,3].The main idea behind these models is to create in phase space a heteroclinic network – a set of saddle points(or cycles)connected by one-dimensional unstable separatrices.In this work,we consider networks of neuronlike units that display sequences of spiking patterns due to an alternative mechanism which does not involve the heteroclinic network but is based on dynamic bifurcations [4,5].The switching dynamics is presented as transitions between metastable states,regular or chaotic.Each metastable state is formed by a group of elements(a cluster)simultaneously fired during some finite time.The activation of an individual element is related to a phase trajectory(of a partial subsystem)attracted to a stable limit cycle(chaotic attractor)that in a little while disappears through a dynamic bifurcation [6,7].After some time delay,the trajectory leaves that region,and the corresponding element ceases to be active.To describe spontaneous switching between different patterns of cluster activation,we propose a model of coevolving networks.In this case,the network topology evolves according to the dynamics of the elements,and the ordering of switching depends on the topology.As a result,during some time the system stays in a cluster state,i.e.,displays a repeating sequence of fired elements in a particular order; after that,the system enters another cluster state and stays there for a while.Such a transient process in a network with evolving topology enables to describe complex transitions: first,the transitions between the clusters – simultaneous activities of different elements,and second,the transitions between the cluster states – cycling switching of clusters in a fixed order.