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We propose a new method for quantitative characterization of spatial network-like patterns with loops, such as surface fracture patterns, leaf vein networks and patterns of urban streets. Such patterns are not well characterized by purely…

We study the emergence of chimera states in a multilayer neuronal network, where one layer is composed of coupled and the other layer of uncoupled neurons. Through the multilayer structure, the layer with coupled neurons acts as the medium…

The emergence of order in collective dynamics is a fascinating phenomenon that characterizes many natural systems consisting of coupled entities. Synchronization is such an example where individuals, usually represented by either linear or…

Spiral waves are ubiquitous in two-dimensional systems of chemical or biological oscillators coupled locally by diffusion. At the center of such spirals is a phase singularity, a topological defect where the oscillator amplitude drops to…

The chimera state with co-existing coherent-incoherent dynamics has recently attracted a lot of attention due to its wide applicability. We investigate non-locally coupled identical chaotic maps with delayed interactions in the multiplex…

We investigate numerically the time dependence of the multiple quantum coherences and entanglement in linear chains up to nine nuclear spins of 1/2 coupled by the dipole-dipole interactions. Two models are considered: (1) a spin chain with…

We investigate the basin of attraction properties and its boundaries for chimera states in a circulant network of H\'enon maps. Chimera states, for which coherent and incoherent domains coexist, emerge as a consequence of the coexistence of…

In a network of coupled oscillators, a symmetry-broken dynamical state characterized by the coexistence of coherent and incoherent parts can spontaneously form. It is known as a chimera state. We study chimera states in a network consisting…

We investigate the synchronization behavior and the emergence of chimera states in a system of two interacting populations of maps possessing chaotic neural-like dynamics. We characterize four collective states on the space of coupling…

We consider classical hard-core particles moving on two parallel chains in the same direction. An interaction between the channels is included via the hopping rates. For a ring, the stationary state has a product form. For the case of…

In this work, two-cluster modes are studied in a system of globally coupled Kuramoto-Sakaguchi phase oscillators with inertia. It is shown that these regimes can be of two types: with a constant intercluster phase difference rotating at the…

More than a decade ago, a surprising coexistence of synchronous and asynchronous behavior called the chimera state was discovered in networks of nonlocally coupled identical phase oscillators. In later years, chimeras were found to occur in…

We study the dynamics of one--dimensional discrete models of one--component active medium built up of spatially inhomogeneous chains of diffusively coupled piecewise linear maps. The nonhomogeneities (``defects'') are treated in terms of…

The appearance of infinitely-many period-doubling cascades is one of the most prominent features observed in the study of maps depending on a parameter. They are associated with chaotic behavior, since bifurcation diagrams of a map with a…

We investigate an array of identical phase oscillators non-locally coupled without time delay, and find that chimera state with two coherent clusters exists which is only reported in delay-coupled systems previously. Moreover, we find that…

Numerous studies have reported two types of doubling of invariant closed curves (ICCs) in dynamical systems: (a) the creation of two disjoint ICCs such that iterations flip between them; and (b) the creation of a single ICC of double the…

We study a network of three populations of coupled phase oscillators with identical frequencies. The populations interact nonlocally, in the sense that all oscillators are coupled to one another, but more weakly to those in neighboring…

Collective organisation of patterns into ring-like configurations has been well-studied when patterns are subject to either weak or semi-strong interactions. However, little is known numerically or analytically about their formation when…

Chimeras occur in networks of two coupled populations of oscillators when the oscillators in one population synchronise while those in the other are asynchronous. We consider chimeras of this form in networks of planar oscillators for which…

Networks of identical, symmetrically coupled oscillators can spontaneously split into synchronized and desynchronized sub-populations. Such chimera states were discovered in 2002, but are not well understood theoretically. Here we obtain…