Related papers: Benjamin-Feir instabilities on directed networks
Several mechanisms have been proposed to explain the spontaneous generation of self-organized patterns, hypothesised to play a role in the formation of many of the magnificent patterns observed in Nature. In several cases of interest, the…
We introduce new algebro-topological invariants of directed networks, based on the topological construction of the directed clique complex. The shape of the underlying directed graph is encoded in a way that can be studied mathematically to…
Regular spatial structures emerge in a wide range of different dynamics characterized by local and/or nonlocal coupling terms. In several research fields this has spurred the study of many models, which can explain pattern formation. The…
In generic Hamiltonian systems with a mixed phase space chaotic transport may be directed and ballistic rather than diffusive. We investigate one particular model showing this behaviour, namely a spatially periodic billiard chain in which…
We present a set of phase-space portraits illustrating the extraordinary oscillatory possibilities of the dynamical systems through the so-called generalized Landau scenario. In its simplest form the scenario develops in N dimensions around…
Oscillator networks display intricate synchronization patterns. Determining their stability typically requires incorporating the symmetries of the network coupling. Going beyond analyses that appeal only to a network's automorphism group,…
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…
From a simple model for the driven motion of a planar interface under the influence of a diffusion field we derive a damped nonlinear oscillator equation for the interface position. Inside an unstable regime, where the damping term is…
Collective dynamics on small-world networks emerge in a broad range of systems with their spectra characterizing fundamental asymptotic features. Here we derive analytic mean field predictions for the spectra of small-world models that…
Pattern formation mechanisms of a reaction-diffusion-advection system, with one diffusivity, differential advection, and (Robin) boundary conditions of Danckwerts type, are being studied. Pattern selection requires mapping the domains of…
We consider directed networks of Winfree oscillators with power law distributed in- and out-degree distributions. Gaussian and power law distributed intrinsic frequencies are considered, and these frequencies are positively correlated with…
We study the effect of adding to a directed chain of interconnected systems a directed feedback from the last element in the chain to the first. The problem is closely related to the fundamental question of how a change in network topology…
Nonreciprocal interactions fundamentally alter the collective dynamics of nonlinear oscillator networks. Here we investigate Stuart-Landau oscillators on a ring with nonreciprocal reactive or dissipative couplings combined with Kerr-type or…
An anomalous mean-field solution is known to capture the non trivial phase diagram of the Ising model in annealed complex networks. Nevertheless the critical fluctuations in random complex networks remain mean-field. Here we show that a…
We study the instability of the spectrum for a class of non-selfadjoint anharmonic oscillators, estimating the behavior of the instability indices (i. e. the norm of spectral projections) associated with the large eigenvalues of these…
Pattern-forming fronts are often controlled by an external stimulus which progresses through a stable medium at a fixed speed, rendering it unstable in its wake. By controlling the speed of excitation, such stimuli, or "triggers," can…
The topological nature of the disorder of glasses and supercooled liquids strongly affects their high-frequency dynamics. In order to understand its main features, we analytically studied a simple topologically disordered model, where the…
In network theory, a question of prime importance is how to assess network vulnerability in a fast and reliable manner. With this issue in mind, we investigate the response to parameter changes of coupled dynamical systems on complex…
Networks of coupled degrade-and-fire (DF) oscillators are simple dynamical models of assemblies of interacting self-repressing genes. For mean-field interactions, which most mathematical studies have assumed so far, every trajectory must…
A quantitative evaluation of the contribution of individual units in producing the collective behavior of a complex network can allow us to understand the potential damage to the structure integrity due to the failure of local nodes. Given…