ABSTRACT
We considered a network consisting of two populations of phase oscillators, the interaction of which is determined by different rules for the coupling adaptation. The introduction of various adaptation rules leads to the suppression of splay states and the emergence of each population complex non-stationary behavior called transient circulant clusters. In such states, each population contains a pair of anti-phase clusters whose size and composition slowly change over time as a result of successive transitions of oscillators between clusters. We show that an increase in the mismatch of the adaptation rules makes it possible to stop the process of rearrangement of clusters in one or both populations of the network. Transitions to such modes are always preceded by the appearance of solitary states in one of the populations.
ABSTRACT
We study the interaction of chimera states in multiplex two-layer systems, where each layer represents a network of interacting phase oscillators with adaptive couplings. A feature of this study is the consideration of synchronization processes for a wide range of chimeras with essentially different properties, which are achieved due to the use of different types of coupling adaptation within isolated layers. We study the effect of forced synchronization of chimera states under unidirectional action between layers. This process is accompanied not only by changes in the frequency characteristics of the oscillators, but also by the transformation of the structure of interactions within the slave layer that become close to the properties of the master layer of the system. We show that synchronization close to identical is possible, even in the case of interaction of chimeras with essentially different structural properties (number and size of coherent clusters) formed by means of a relatively large parameter mismatch between the layers. In the case of mutual action of the layers in chimera states, we found a number of new scenarios of the multiplex system behavior along with those already known, when identical or different chimeras appear in both layers. In particular, we have shown that a fairly weak interlayer coupling can lead to suppression of the chimera state when one or both layers of the system demonstrate an incoherent state. On the contrary, a strong interlayer coupling provides a complete synchronization of the layer dynamics, accompanied by the appearance of multicluster states in the system's layers.
ABSTRACT
We report the phenomenon of self-organized emergence of hierarchical multilayered structures and chimera states in dynamical networks with adaptive couplings. This process is characterized by a sequential formation of subnetworks (layers) of densely coupled elements, the size of which is ordered in a hierarchical way, and which are weakly coupled between each other. We show that the hierarchical structure causes the decoupling of the subnetworks. Each layer can exhibit either a two-cluster state, a periodic traveling wave, or an incoherent state, and these states can coexist on different scales of subnetwork sizes.
ABSTRACT
We have developed a new approach for the description of sequential dynamics of excitatory neural networks. Our approach is based on the dynamics of synapses possessing the short-term plasticity property. We suggest a model of such synapses in the form of a second-order system of nonlinear ODEs. In the framework of the model two types of responses are realized-the fast and the slow ones. Under some relations between their timescales a cellular automaton (CA) on the graph of connections is constructed. Such a CA has only a finite number of attractors and all of them are periodic orbits. The attractors of the CA determine the regimes of sequential dynamics of the original neural network, i.e., itineraries along the network and the times of successive firing of neurons in the form of bunches of spikes. We illustrate our approach on the example of a Morris-Lecar neural network.