Dissipation-induced instabilities in an optical cavity laser: A mechanical analog near the 1:1 resonance

The 1:1 resonance for perturbed Hamiltonian systems with small dissipative and energy injection terms has been studied. These perturbations of the 1:1 resonance exhibit dissipation induced instabilities. This mechanism allows one to show that an optical cavity with small pumping is unstable when one takes into account the dissipative effects. The Maxwell-Bloch equations are the asymptotic normal form that describe this instability when energy is injected through forcing at zero frequency. A simple mechanical system close to the 1:1 resonance has been displayed, which is a mechanical analog of the laser

Spin-transfer-driven nano-oscillators are equivalent to parametric resonators

The equivalence between different physical systems permits us to transfer knowledge between them and to characterize the universal nature of their dynamics. We demonstrate that a nanopillar driven by a spin-transfer torque is equivalent to a rotating magnetic plate, which permits us to consider the nanopillar as a macroscopic system under a time-modulated injection of energy, that is, a simple parametric resonator. This equivalence allows us to characterize the phases diagram and to predict magnetic states and dynamical behaviors, such as solitons, stationary textures, and oscillatory localized states, among others. Numerical simulations confirm these predictions.Comment: 8 pages, 7 figure

Transversal interface dynamics of a front connecting a stripe pattern to a uniform state

Interfaces in two-dimensional systems exhibit unexpected complex dynamical behaviors, the dynamics of a border connecting a stripe pattern and a uniform state is studied. Numerical simulations of a prototype isotropic model, the subcritical Swift-Hohenberg equation, show that this interface has transversal spatial periodic structures, zigzag dynamics and complex coarsening process. Close to a spatial bifurcation, an amended amplitude equation and a one-dimensional interface model allow us to characterize the dynamics exhibited by this interface.Comment: 4 pages. To be published in Europhysics Letter

Extended patchy ecosystems may increase their total biomass through self-replication

Patches of vegetation consist of dense clusters of shrubs, grass, or trees, often found to be circular characteristic size, defined by the properties of the vegetation and terrain. Therefore, vegetation patches can be interpreted as localized structures. Previous findings have shown that such localized structures can self-replicate in a binary fashion, where a single vegetation patch elongates and divides into two new patches. Here, we extend these previous results by considering the more general case, where the plants interact non-locally, this extension adds an extra level of complexity and shrinks the gap between the model and real ecosystems, where it is known that the plant-to-plant competition through roots and above-ground facilitating interactions have non-local effects, i.e. they extend further away than the nearest neighbor distance. Through numerical simulations, we show that for a moderate level of aridity, a transition from a single patch to periodic pattern occurs. Moreover, for large values of the hydric stress, we predict an opposing route to the formation of periodic patterns, where a homogeneous cover of vegetation may decay to spot-like patterns. The evolution of the biomass of vegetation patches can be used as an indicator of the state of an ecosystem, this allows to distinguish if a system is in a self-replicating or decaying dynamics. In an attempt to relate the theoretical predictions to real ecosystems, we analyze landscapes in Zambia and Mozambique, where vegetation forms patches of tens of meters in diameter. We show that the properties of the patches together with their spatial distributions are consistent with the self-organization hypothesis. We argue that the characteristics of the observed landscapes may be a consequence of patch self-replication, however, detailed field and temporal data is fundamental to assess the real state of the ecosystems.Comment: 38 pages, 12 figures, 1 tabl

Spatiotemporal chaos induces extreme events in an extended microcavity laser

Extreme events such as rogue wave in optics and fluids are often associated with the merging dynamics of coherent structures. We present experimental and numerical results on the physics of extreme events appearance in a spatially extended semiconductor microcavity laser with intracavity saturable absorber. This system can display deterministic irregular dynamics only thanks to spatial coupling through diffraction of light. We have identified parameter regions where extreme events are encountered and established the origin of this dynamics in the emergence of deterministic spatiotemporal chaos, through the correspondence between the proportion of extreme events and the dimension of the strange attractor