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 ...

Bursting neurons fire rapid sequences of action potential spikes followed by a quiescent period. The basic dynamical mechanism of bursting is the slow currents that modulate a fast spiking activity caused by rapid ionic currents. Minimal models of bursting neurons must include both effects. We considered one of these models and its relation with a generalized Kuramoto model, thanks to the defin...

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...

We consider ensembles of sine-coupled phase oscillators consisting of subpopulations of identical units, with a general heterogeneous coupling between subpopulations. Using the Watanabe-Strogatz ansatz we reduce the dynamics of the ensemble to a relatively small number of dynamical variables plus microscopic constants of motion. This reduction is independent of the sizes of subpopulations and r...

The conventional chaos control is only to reach single control objective at each time. Different control objective only can be realized at another time. Obviously, that is not enough for applications of chaos control, especially for chaotic connected complex networks. Therefore multi-objective control (MOC) and cluster synchronization are naturally raised and deeded in practice, as well as some...