We investigate the bifurcation structure of the Kuramoto-Sivashinsky equation with homogeneous Dirichlet boundary conditions. Using hidden symmetry principles, based on an extended problem with periodic boundary conditions and O(2) symmetry, we show that the zero solution exhibits two kinds of pitchfork bifurcations: one that breaks the reflection symmetry of the system with Dirichlet boundary ...

Collective violence in direct confrontations between two opposing groups happens in short bursts wherein small subgroups briefly attack small numbers of opponents, while the majority of participants forms a supportive audience. These bursts and subgroups’ small sizes are explained by Kuramoto’s synchronization model.

A model consisting of a mixed Kuramoto Sivashinsky Korteweg de Vries equation, linearly coupled to an extra linear dissipative equation, is proposed. The model applies to the description of surface waves on multilayered liquid films. The extra equation makes its possible to stabilize the zero solution in the model, thus opening way to the existence of stable solitary pulses (SPs). By means of t...

We examine the problem of predicting the evolution of solutions of the KuramotoSivashinsky equation when initial data are missing. We use the optimal prediction method to construct equations for the reduced system. The resulting equations for the resolved components of the solution are random integrodifferential equations. The accuracy of the predictions depends on the type of projection used i...

Many coordination phenomena are based on a synchronisation process, whose global behaviour emerges from the interactions among the individual parts. Often in Nature, such self-organising mechanism allows the system to behave as a whole and thus grounding its very first existence, or expected functioning, on such process. There are however cases where synchronisation acts against the stability o...

This article is concerned with a Kuramoto–Sivashinsky-Korteweg-de Vries equation in bounded interval. The as well one of the boundary conditions are supposed to be subject presence parameter $ \nu> 0 $. Moreover, this specific condition has time-delay effect. As \nu tends zero, we show that can obtain findings [4,58] concerning two Korteweg–de equations. Indeed, able retrieve well-posedness ...

We investigate the limit sets of a network of coupled Kuramoto oscillators with a coupling matrix determined by a Hebb rule. These limit sets are the output of the network if used for the recognition of a defective binary pattern out of several given patterns, with the output pattern encoded in the oscillators’ phases. We show that if all pairs of given patterns have maximum Hamming distance, t...