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.

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.

Emergence of spatiotemporal dislocation chains in drifting patterns.

One-dimensional patterns subjected to counter-propagative flows or speed jumps exhibit a rich and complex spatiotemporal dynamics, which is characterized by the perpetual emergence of spatiotemporal dislocation chains. Using a universal amplitude equation of drifting patterns, we show that this behavior is a result of a combination of a phase instability and an advection process caused by an inhomogeneous drift force. The emergence of spatiotemporal dislocation chains is verified in numerical simulations on an optical feedback system with a non-uniform intensity pump. Experimentally this phenomenon is also observed in a tilted quasi-one-dimensional fluidized shallow granular bed mechanically driven by a harmonic vertical vibration.

Spatially modulated kinks in shallow granular layers.

We report on the experimental observation of spatially modulated kinks in a shallow one-dimensional fluidized granular layer subjected to a periodic air flow. We show the appearance of these solutions as the layer undergoes a parametric instability. Due to the inherent fluctuations of the granular layer, the kink profile exhibits an effective wavelength, a precursor, which modulates spatially the homogeneous states and drastically modifies the kink dynamics. We characterize the average and fluctuating properties of this solution. Finally, we show that the temporal evolution of these kinks is dominated by a hopping dynamics, related directly to the underlying spatial structure.

Origin of the pinning of drifting monostable patterns.

Under drift forces, a monostable pattern propagates. However, examples of nonpropagative dynamics have been observed. We show that the origin of this pinning effect comes from the coupling between the slow scale of the envelope to the fast scale of the modulation of the underlying pattern. We evidence that this effect stems from spatial inhomogeneities in the system. Experiments and numerics on drifting pattern-forming systems subjected to inhomogeneous spatial pumping or boundary conditions confirm this origin of pinning dynamics.