Quiescent Gap Solitons in Coupled Nonuniform Bragg Gratings with Cubic-Quintic Nonlinearity

We study the stability characteristics of zero-velocity gap solitons in dual-core Bragg gratings with cubic-quintic nonlinearity and dispersive reflectivity. The model supports two disjointed families of gap solitons (Type 1 and Type 2). Additionally, asymmetric and symmetric solitons exist in both Type 1 and Type 2 families. A comprehensive numerical stability analysis is performed to analyze the stability of solitons. It is found that dispersive reflectivity improves the stability of both types of solitons. Nontrivial stability boundaries have been identified within the bandgap for each family of solitons. The effects and interplay of dispersive reflectivity and the coupling coefficient on the stability regions are also analyzed.

Amplitude death and restoration in networks of oscillators with random-walk diffusion

Systems composed of reactive particles diffusing in a network display emergent dynamics. While Fick’s diffusion can lead to Turing patterns, other diffusion schemes might display more complex phenomena. Here we study the death and restoration of collective oscillations in networks of oscillators coupled by random-walk diffusion, which modifies both the original unstable fixed point and the stable limit-cycle, making them topology-dependent. By means of numerical simulations we show that, in some cases, the diffusion-induced heterogeneity stabilizes the initially unstable fixed point via a Hopf bifurcation. Further increasing the coupling strength can moreover restore the oscillations. A numerical stability analysis indicates that this phenomenology corresponds to a case of amplitude death, where the inhomogeneous stabilized solution arises from the interplay of random walk diffusion and heterogeneous topology. Our results are relevant in the fields of epidemic spreading or ecological dispersion, where random walk diffusion is more prevalent.