Nonlocality-induced front interaction enhancement

We demonstrate that nonlocal coupling strongly influences the dynamics of fronts connecting two equivalent states. In two prototype models we observe a large amplification in the interaction strength between two opposite fronts increasing front velocities several orders of magnitude. By analyzing the spatial dynamics we prove that way beyond quantitative effects, nonlocal terms can also change the overall qualitative picture by inducing oscillations in the front profile. This leads to a mechanism for the formation of localized structures not present for local interactions. Finally, nonlocal coupling can induce a steep broadening of localized structures, eventually annihilating them.Comment: 4 pages, 6 figure

A compartmental model for Xylella fastidiosa diseases with explicit vector seasonal dynamics

The bacterium Xylella fastidiosa (Xf) is mainly transmitted by the spittlebug, Philaenus spumarius, in Europe, where it has caused significant economic damage to olive and almond trees. Understanding the factors that determine disease dynamics in pathosystems that share similarities can help design control strategies focused on minimizing transmission chains. Here we introduce a compartmental model for Xf-caused diseases in Europe that accounts for the main relevant epidemiological processes, including the seasonal dynamics of P. spumarius. The model was confronted with epidemiological data from the two major outbreaks of Xf in Europe, the olive quick disease syndrome (OQDS) in Apulia, Italy, caused by the subspecies pauca, and the almond leaf scorch disease (ALSD) in Majorca, Spain, caused by subspecies multiplex and fastidiosa. Using a Bayesian inference framework, we show how the model successfully reproduces the general field data in both diseases. In a global sensitivity analysis, the vector-plant and plant-vector transmission rates, together with the vector removal rate, were the most influential parameters in determining the time of the infected host population peak, the incidence peak and the final number of dead hosts. We also used our model to check different vector-based control strategies, showing that a joint strategy focused on increasing the rate of vector removal while lowering the number of annual newborn vectors is optimal for disease control.Comment: 18 pages, 8 figure

Spatial effects in parasite-induced marine diseases of immobile hosts

Emerging marine infectious diseases pose a substantial threat to marine ecosystems and the conservation of their biodiversity. Compartmental models of epidemic transmission in marine sessile organisms, available only recently, are based on non-spatial descriptions in which space is homogenized and parasite mobility is not explicitly accounted for. However, in realistic scenarios epidemic transmission is conditioned by the spatial distribution of hosts and the parasites' mobility patterns, calling for an explicit description of space. In this work, we develop a spatially explicit individual-based model to study disease transmission by waterborne parasites in sessile marine populations. We investigate the impact of spatial disease transmission through extensive numerical simulations and theoretical analysis. Specifically, the effects of parasite mobility into the epidemic threshold and the temporal progression of the epidemic are assessed. We show that larger values of pathogen mobility imply more severe epidemics, as the number of infections increases, and shorter timescales to extinction. An analytical expression for the basic reproduction number of the spatial model, R~0, is derived as a function of the non-spatial counterpart, R 0, which characterizes a transition between a disease-free and a propagation phase, in which the disease propagates over a large fraction of the system.Fil: Giménez Romero, Àlex. Consejo Superior de Investigaciones Científicas. Instituto de Física Interdisciplinar y Sistemas Complejos; EspañaFil: Vazquez, Federico. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; Argentina. Consejo Superior de Investigaciones Científicas. Instituto de Física Interdisciplinar y Sistemas Complejos; EspañaFil: López, Cristóbal. Consejo Superior de Investigaciones Científicas. Instituto de Física Interdisciplinar y Sistemas Complejos; EspañaFil: Matías, Manuel A.. Consejo Superior de Investigaciones Científicas. Instituto de Física Interdisciplinar y Sistemas Complejos; Españ

Dynamics of localized and patterned structures in the Lugiato-Lefever equation determine the stability and shape of optical frequency combs

It has been recently uncovered that coherent structures in microresonators such as cavity solitons and patterns are intimately related to Kerr frequency combs. In this work, we present a general analysis of the regions of existence and stability of cavity solitons and patterns in the Lugiato-Lefever equation, a mean-field model that finds applications in many different nonlinear optical cavities. We demonstrate that the rich dynamics and coexistence of multiple solutions in the Lugiato-Lefever equation are of key importance to understanding frequency comb generation. A detailed map of how and where to target stable Kerr frequency combs in the parameter space defined by the frequency detuning and the pump power is provided. Moreover, the work presented also includes the organization of various dynamical regimes in terms of bifurcation points of higher codimension in regions of parameter space that were previously unexplored in the Lugiato-Lefever equation. We discuss different dynamical instabilities such as oscillations and chaotic regimes.This research was supported by the Research Foundation-Flanders (FWO), by the Spanish MINECO, and FEDER under Grants FISICOS (Grant No. FIS2007-60327) and INTENSE@COSYP (Grant No. FIS2012-30634), by Comunitat Autonoma de les Illes Balears, by the Research Council of the Vrije Universiteit Brussel (VUB), and by the Belgian Science Policy Office (BelSPO) under Grant No. IAP 7-35. S. Coen also acknowledges the support of the Marsden Fund of the Royal Society of New Zealand.Peer reviewe

Effects of a localized beam on the dynamics of excitable cavity solitons

We study the dynamical behavior of dissipative solitons in an optical cavity filled with a Kerr medium when a localized beam is applied on top of the homogeneous pumping. In particular, we report on the excitability regime that cavity solitons exhibits which is emergent property since the system is not locally excitable. The resulting scenario differs in an important way from the case of a purely homogeneous pump and now two different excitable regimes, both Class I, are shown. The whole scenario is presented and discussed, showing that it is organized by three codimension-2 points. Moreover, the localized beam can be used to control important features, such as the excitable threshold, improving the possibilities for the experimental observation of this phenomenon.Comment: 9 Pages, 12 figure

Rare Events and Scale--Invariant Dynamics of Perturbations in Delayed Dynamical Systems

We study the dynamics of perturbations in time delayed dynamical systems. Using a suitable space-time coordinate transformation, we find that the time evolution of the linearized perturbations (Lyapunov vector) can be mapped to the linear Zhang surface growth model [Y.-C. Zhang, J. Phys. France {\bf 51}, 2129 (1990)], which is known to describe surface roughening driven by power-law distributed noise. As a consequence, Lyapunov vector dynamics is dominated by rare random events that lead to non-Gaussian fluctuations and multiscaling properties.Comment: Final version to appear in Phys. Rev. Lett., 4 pages, 3 eps fig

Phase-space structure of two-dimensional excitable localized structures

In this work we characterize in detail the bifurcation leading to an excitable regime mediated by localized structures in a dissipative nonlinear Kerr cavity with a homogeneous pump. Here we show how the route can be understood through a planar dynamical system in which a limit cycle becomes the homoclinic orbit of a saddle point (saddle-loop bifurcation). The whole picture is unveiled, and the mechanism by which this reduction occurs from the full infinite-dimensional dynamical system is studied. Finally, it is shown that the bifurcation leads to an excitability regime, under the application of suitable perturbations. Excitability is an emergent property for this system, as it emerges from the spatial dependence since the system does not exhibit any excitable behavior locally.Comment: 10 pages, 9 figure

Dynamics on Complex Networks and Applications

At the eight-year anniversary of Watts & Strogatz's work on the collective dynamics of small-world networks and seven years after Barabasi & Albert's discovery of scale-free networks, the area of dynamical processes on complex networks is at the forefront of the current research on nonlinear dynamics and complex systems. This volume brings together a selection of original contributions in complementary topics of statistical physics, nonlinear dynamics and biological sciences, and is expected to provide the reader with a comprehensive up-to-date representation of this rapidly developing area.Comment: Preface article of the Physica D Special Issue "Dynamics on Complex Networks and Applications" (4 pages). Full issue available at http://www.sciencedirect.com/science/journal/0167278

Formation of stellar inner discs and rings in spiral galaxies through minor mergers

Recent observations show that inner disks and rings (IDs and IRs) are not preferentially found in barred galaxies, pointing to the relevance of formation mechanisms different to the traditional bar-origin scenario. Nevertheless, the role of minor mergers in the formation of these inner components (ICs), while often invoked, is still poorly understood. We have investigated the capability of minor mergers to trigger the formation of IDs and IRs in spiral galaxies through collisionless N-body simulations. Our models prove that minor mergers are an efficient mechanism to form rotationally-supported stellar ICs in spirals, neither requiring strong dissipation nor noticeable bars, and suggest that their role in the formation of ICs must have been much more complex than just bar triggering