S. Coulibaly

Chimera-type states induced by local coupling.

Coupled oscillators can exhibit complex self-organization behavior such as phase turbulence, spatiotemporal intermittency, and chimera states. The latter corresponds to a coexistence of coherent and incoherent states apparently promoted by nonlocal or global coupling. Here we investigate the existence, stability properties, and bifurcation diagram of chimera-type states in a system with local coupling without different time scales. Based on a model of a chain of nonlinear oscillators coupled to adjacent neighbors, we identify the required attributes to observe these states: local coupling and bistability between a stationary and an oscillatory state close to a homoclinic bifurcation. The local coupling prevents the incoherent state from invading the coherent one, allowing concurrently the existence of a family of chimera states, which are organized by a homoclinic snaking bifurcation diagram.

Soliton pair interaction law in parametrically driven Newtonian fluid

An experimental and theoretical study of the motion and interaction of the localized excitations in a vertically driven small rectangular water container is reported. Close to the Faraday instability, the parametrically driven damped nonlinear Schrödinger equation models this system. This model allows one to characterize the pair interaction law between localized excitations. Experimentally we have a good agreement with the pair interaction law.

Localized waves in a parametrically driven magnetic nanowire

The pattern formation in a magnetic wire forced by a transversal uniform and oscillatory magnetic field is studied. This system is described in the continuous framework by the Landau-Lifshitz-Gilbert equation. We find numerically that, the spatio-temporal magnetization field exhibits a family of localized states that connect asymptotically a uniform oscillatory state with an extended wave. Close to parametrical resonance instability, an amended amplitude equation is derived, which allows us to understand and characterize these localized waves.

Interaction law of 2D localized precession states

A theoretical study of the interaction of localized precession states on an easy-plane ferromagnetic layer submitted to a magnetic field that combines a constant and an oscillating part is reported. Within the framework the Landau-Lifshitz-Gilbert equation, we perform a comparison of analytical studies and micromagnetic simulations. Close to the parametric resonance, the parametrically driven damped nonlinear Schrodinger equation models this system. By means of this amplitude equation we are able to characterize the localized precession states and their pair interaction law. Numerically, we have a good agreement with the pair interaction law.

Two-soliton precession state in a parametrically driven magnetic wire

The pattern formation in a magnetic wire forced by a time dependent magnetic field is studied. This system is described in the continuum limit by the Landau-Lifshitz-Gilbert equation. The spatio-temporal magnetization field exhibits two-soliton bound state solutions. Close to the parametric resonance instability, an amplitude equation allows us to understand and characterize these localized states.

Recurrent noise-induced phase singularities in drifting patterns

We show that the key ingredients for creating recurrent traveling spatial phase defects in drifting patterns are a noise-sustained structure regime together with the vicinity of a phase transition, that is, a spatial region where the control parameter lies close to the threshold for pattern formation. They both generate specific favorable initial conditions for local spatial gradients, phase, and/or amplitude. Predictions from the stochastic convective Ginzburg-Landau equation with real coefficients agree quite well with experiments carried out on a Kerr medium submitted to shifted optical feedback that evidence noise-induced traveling phase slips and vortex phase-singularities.