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Oscillatory dynamics of complex networks has recently attracted great attention. In this paper we study pattern formation in oscillatory complex networks consisting of excitable nodes. We find that there exist a few center nodes and small…

We study wave propagation in networks of coupled cells which can behave as excitable or self-oscillatory media. For excitable media, an asymptotic construction of wave trains is presented. This construction predicts their shape and speed,…

Recently, self-sustained oscillations in complex networks consisting of nonoscillatory nodes (network oscillators) have attracted great interest in diverse natural and social fields. Due to complexity of network behaviors, little is known…

We identify a new type of pattern formation in spatially distributed active systems. We simulate one-dimensional two-component systems with predator-prey local interaction and pursuit-evasion taxis between the components. In a sufficiently…

We examine traveling-wave solutions on a regular ring network with one additional long-range link that spans a distance d. The nodes obey the FitzHugh-Nagumo kinetics in the excitable regime. The additional shortcut induces a plethora of…

The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent…

We study the relationship between the modularity of scale-free excitable networks and their ability to support self-sustained oscillation patterns. We find that the probability for a network of given degree-distribution exponent to be able…

We study the response of an ensemble of synchronized phase oscillators to an external harmonic perturbation applied to one of the oscillators. Our main goal is to relate the propagation of the perturbation signal to the structure of the…

A novel discrete model (D-model) is presented describing nonlinear wave interactions in systems with small and moderate nonlinearity under narrow frequency band excitation. It integrates in a single theoretical frame two mechanisms of…

Robust coordination and organization in large ensembles of nonlinear oscillatory units play a vital role in a wide range of natural and engineered system. The control of self-organizing network-coupled systems has recently seen significant…

We investigate different emergent dynamics namely oscillation quenching and revival of oscillation in a global network of identical oscillators coupled with diffusive (positive) delay coupling as it is perturbed by symmetry breaking…

There is enormous interest -- both mathematically and in diverse applications -- in understanding the dynamics of coupled oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology,…

The control of network-coupled nonlinear dynamical systems is an active area of research in the nonlinear science community. Coupled oscillator networks represent a particularly important family of nonlinear systems, with applications…

A computer model is described which is used to assess the dynamical complexity of a class of networks of spiking neurons with small-world properties. Networks are constructed by forming an initially segregated set of highly intra-connected…

We study the dynamics of excitable integrate-and-fire neurons in a small-world network. At low densities $p$ of directed random connections, a localized transient stimulus results in either self-sustained persistent activity or in a brief…

A networked oscillator based analysis is performed for periodic bluff body flows to examine and control the transfer of kinetic energy. Spatial modes extracted from the flow field with corresponding amplitudes form a set of oscillators…

Living neural networks in our brains autonomously self-organize into large, complex architectures during early development to result in an organized and functional organic computational device. A key mechanism that enables the formation of…

Recent work found distributed resonances in driven oscillator networks and AC power grids. The emerging dynamic resonance patterns are highly heterogeneous and nontrivial, depending jointly on the driving frequency, the interaction topology…

We investigate the dynamic behavior of lattices with disorder introduced through non-local network connections. Inspired by the Watts-Strogatz small-world model, we employ a single parameter to determine the probability of local connections…

We suggest the numerical approach to detect eigenfrequencies of trapped modes in waveguides or guided waves in diffraction gratings. At the same time, the approach works perfectly for computation of systems with finitely many scattering…