Related papers: Complex behavior in chains of nonlinear oscillator…
Network theory is rapidly changing our understanding of complex systems, but the relevance of topological features for the dynamic behavior of metabolic networks, food webs, production systems, information networks, or cascade failures of…
We investigate emergence of the global collective behavior in networks of diffusively coupled identical oscillators, which in the established model is an invariant manifold of the motion equations. The interaction is modeled with the graph…
Using recent dimensionality reduction techniques in large systems of coupled phase oscillators exhibiting bistability, we analyze complex macroscopic behavior arising when the coupling between oscillators is allowed to evolve slowly as a…
We study the emergence and coherence of stochastic oscillations in star networks of excitable elements in which peripheral nodes receive independent random inputs. A biophysical model of a distal branch of sensory neuron in which peripheral…
We consider two neuronal networks coupled by long-range excitatory interactions. Oscillations in the gamma frequency band are generated within each network by local inhibition. When long-range excitation is weak, these oscillations…
When a dynamical system contains several different modes of oscillations it may behave in a variety of ways: If the modes oscillate at their own individual frequencies, it exhibits quasiperiodic behavior; when the modes lock to one another…
A complex collective emerging behavior characterized by coexisting coherent and incoherent do- mains is termed as a chimera state. We bring out the existence of a new type of chimera in a nonlocally coupled ensemble of identical oscillators…
Does the assignment order of a fixed collection of slightly distinct subsystems into given communication channels influence the overall ensemble behavior? We discuss this question in the context of complex networks of non-identical…
The collective behavior of the ensembles of coupled nonlinear oscillator is one of the most interesting and important problems in modern nonlinear dynamics. In this paper, we study rotational dynamics, in particular space-time structures,…
We show that subsets of interacting oscillators may synchronize in different ways within a single network. This diversity of synchronization patterns is promoted by increasing the heterogeneous distribution of coupling weights and/or…
Oscillatory activity is ubiquitous in natural and engineered network systems. The interaction scheme underlying interdependent oscillatory components governs the emergence of network-wide patterns of synchrony that regulate and enable…
We investigate the emergence of sustained spatio-temporal behaviors in reaction-phase separation systems. We focus on binary systems, in which either one or both species can phase separate, and we discuss the stability of the homogeneous…
We suggest a new perspective of research towards understanding the relations between structure and dynamics of a complex network: Can we design a network, e.g. by modifying the features of units or interactions, such that it exhibits a…
Oscillator networks found in social and biological systems are characterized by the presence of wide ranges of coupling strengths and complex organization. Yet robustness and synchronization of oscillations are found to emerge on…
The conditions under which synchronization is achieved for a one-dimensional ring of identical phase oscillators with Kuramoto-like local coupling are studied. The system is approached in the weakly coupled approximation as phase units.…
Many natural systems are organized as networks, in which the nodes (be they cells, individuals or populations) interact in a time-dependent fashion. The dynamic behavior of these networks depends on how these nodes are connected, which can…
Complex network dynamics have been analyzed with models of systems of coupled switches or systems of coupled oscillators. However, many complex systems are composed of components with diverse dynamics whose interactions drive the system's…
We investigate dynamics and bifurcations in a mathematical model that captures electrochemical experiments on arrays of microelectrodes. In isolation, each individual microelectrode is described by a one-dimensional unit with a bistable…
We show that a complex network of phase oscillators may display interfaces between domains (clusters) of synchronized oscillations. The emergence and dynamics of these interfaces are studied in the general framework of interacting phase…
We study the influence of nonuniform motion of oscillators in a ring chain with nonlocal coupling on their collective dynamics and reveal the mechanism behind the emergence of an atypical chimera state in such systems. The mechanism relies…