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 existence stability Lugiato-Lefever equation, mean-field model finds applications many different nonlinear optical cavities. We demonstrate rich dynamics coexistence multiple solutions equation key importance understanding comb generation. A detailed map how where target...

We present a new method that allows one to stabilize chaotic systems by applying proportional pulses the system variables. The does not require any previous knowledge of dynamics. Acting on variables may be most useful for chemical and biological systems, situations which in some cases it difficult find an accessible parameter.

The behavior of uncoupled chaotic systems under the influence external noise has been subject recent work. Some these studies claim that driven by same do synchronize, while other contradict this conclusion. In work we have undertaken an experimental study effect on identically analog circuits. main conclusion is synchronization induced a nonzero mean signal and not its stochastic character.

We report on the discovery of a transition in rings coupled electronic circuits chaotic regime to collective periodic state characterized by time scale that is between two and three orders faster than corresponding an isolated circuit. This arises from linear instability uniform synchronized ring through symmetric Hopf bifurcation. The same type also observed for other systems, e.g., Lorenz attractors.

We find and characterize an excitability regime mediated by localized structures in a dissipative nonlinear optical cavity. The scenario is that stable exhibit Hopf bifurcation to self-pulsating behavior, followed the destruction of oscillation saddle-loop bifurcation. Beyond this point there excitable under application suitable perturbations. Excitability emerges from spatial dependence since system does not any behavior locally. show whole organized Takens-Bogdanov codimension-2 point.

Clonal reproduction characterizes a wide range of species including clonal plants in terrestrial and aquatic ecosystems, microbes such as bacteria parasitic protozoa, with key role human health ecosystem processes. organisms present particular challenge population genetics because, addition to the possible existence replicates same genotype given sample, some hypotheses concepts underlying classical models are irreconcilable clonality. The genetic structure diversity populations were...

Abstract Pierce’s disease (PD) is a vector-borne caused by the bacteria Xylella fastidiosa , which affects grapevines in Americas. Currently, vineyards continental Europe, world’s largest producer of quality wine, have not yet been affected PD. However, climate change may alter this situation. Here we incorporate latest regional projections into climate-driven epidemiological model to assess risk PD epidemics Europe for different levels global warming. We found significant increase above...

In this contribution a modification of the Pecora-Carroll [Phys. Rev. Lett. 64, 821 (1990)] one-way (or drive-response) synchronization method is suggested, such that both drive and response have same dimensionality. As result, it possible reproduce driving signal with single connection, increasing, thus, number potential connections given system. The main features presented in work are discussed an application to R\"ossler Lorenz models [O. E. R\"ossler, Phys. A 57, 397 (1976); N. Lorenz,...

In this work, we demonstrate that key aspects of the dynamical behavior coral reefs at macro scale, which evolve over time scales centuries, can be accurately described using a model integrates few fundamental ecological and physical mechanisms. The displays excitable generating, among other regimes, traveling pulses waves, result in formation spatial structures resembling those observed real reefs, without involving classical pattern mechanism, like Turing scenario. We conduct an in-depth...

The present work studies the influence of nonlocal spatial coupling on existence localized structures in one-dimensional extended systems. We consider systems described by a real field with that has linear dependence field. Leveraging dynamics we provide general framework to understand effect nonlocality shape fronts connecting two stable states. In particular show terms can induce oscillations front tails, allowing for creation structures, emerge from pinning between fronts. parameter space...

In this work we characterize in detail the bifurcation leading to an excitable regime mediated by localized structures a dissipative nonlinear Kerr cavity with homogeneous pump. Here show how route can be understood through planar dynamical system which limit cycle becomes homoclinic orbit of saddle point (saddle-loop bifurcation). The whole picture is unveiled, and mechanism reduction occurs from full infinite-dimensional studied. Finally, it shown that leads excitability regime, under...

We study the influence of a linear nonlocal spatial coupling on interaction fronts connecting two equivalent stable states in prototypical 1-D real Ginzburg-Landau equation. While for local are always monotonic and therefore dynamical behavior leads to coarsening annihilation pairs fronts, terms can induce oscillations front, allowing creation localized structures, emerging from pinning between fronts. show this three different kernels. The first two, mod-exponential Gaussian,...

We show how to exploit excitable regimes mediated by localized structures (LS) perform AND, OR, and NOT logical operations providing full functionality. Our scheme is general can be implemented in any physical system displaying LS. In particular, LS nonlinear photonic devices used for all-optical computing applications where several reconfigurable logic gates the transverse plane of a single device, allowing parallel computing.

In this work we characterize the dynamical instabilities of localized structures exhibited by a recently introduced [Gelens et al., Phys. Rev. A 75, 063812 (2007)] generalization Lugiato-Lefever model that includes weakly nonlocal response an intracavity metamaterial. rich scenario, in which exhibit different types oscillatory instabilities, tristability, and excitability, including regime conditional excitability system is bistable, presented discussed. Finally, it shown scenario organized...

We show that excitability is generic in systems displaying dissipative solitons when spatial inhomogeneities and drift are present. Thus, which do not have oscillatory states, such as the prototypical Swift-Hohenberg equation, display oscillations type I II adding to system. This rich dynamical behavior arises from interplay between pinning inhomogeneity pulling of drift. The scenario presented here provides a general theoretical understanding regimes reported semiconductor microresonators....

The vector-borne bacterium Xylella fastidiosa is responsible for Pierce's disease (PD), a lethal grapevine that originated in the Americas. international plant trade expanding geographic range of this pathogen, posing new threat to viticulture worldwide. To assess potential incidence PD, we have built dynamic epidemiological model based on response 36 varieties pathogen inoculation assays and vectors' distribution when information available. Key temperature-driven processes, such as PD...

Abstract Coral reefs are under rapid decline due to human pressures such as climate change. Achieving the Kunming-Montreal Global Biodiversity Framework goals, which include restoring 30% of degraded habitats like coral by 2030, requires a comprehensive understanding their extent and structure, has been hitherto lacking. We address this limitation based on unprecedented canonical inventory extracted from Allen Atlas shallow-water tropical reefs. identified total 1,579,772 individual...

We have uncovered a phenomenon in coupled chaotic oscillators where subset of Lyapunov exponents, which are originally zero the absence coupling, can become positive as coupling is increased. This occurs for attractors having multiple scrolls, such Lorenz attractor. argue that due to disturbance relative frequencies with trajectory visits different scrolls An algebraic scaling law obtained relates exponents strength. The appears be universal.

Methods for the calculation of atom-molecule dispersion coefficients are reviewed, with emphasis on approximate techniques. New results reported interaction several S-state atoms ground-state molecular hydrogen using Padé bounding technique. The scarcity data dependence intramolecular coordinate imposes use schemes to interpolate and extrapolate coefficient regions where it is unknown. Several approaches suggested based Unsöld approximation Kirkwood variational method.

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

We consider the behavior of rings unidirectionally coupled chaotic systems. When number oscillators in ring is below a certain critical synchronized, while above this threshold an instability appears. The novel feature that may yield rotating wave if some conditions are fulfilled.

We study the behavior of arrays unidirectionally coupled Lorenz systems in chaotic regime. In case rings an instability uniform synchronized state leads to appearance a periodic rotating wave through symmetric Hopf bifurcation. From theoretical grounds it is argued that this must also manifest linear arrays. Numerically shown happens transient way, leading unexpected consequences velocity synchronization, becomes larger.