Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 1912.10875

Interaction between localized vegetation patches and gaps in water-limited environments

M. Tlidi·E. Berrios-Caro·D. Pinto-Ramo·A. G. Vladimirov·M. Clerc
View original source ↗Read source document ↗Export metadata ↓

Abstract

Close to the critical point associated with nascent of bistability and large wavelength pattern forming regime, {\it the Lifshitz point}, the dynamics of many ecological spatially extended systems can be reduced to a simple partial differential equation. This weak gradient approximation is greatly useful for the investigation of localized vegetation patches and gaps. In this contribution, we present a general derivation of the most simple vegetation model without any specification of the shape of Kernel used to describe the facilitative and the competitive interactions between individual plants. The coefficients of the obtained model depend on the choice of the form of the Kernel under consideration. Based on this simple vegetation model, we focus more on gaps and patches interaction. In the case of gaps, the interaction alternates between attractive and repulsive depending on the distance separating the gaps. This allows for the stabilization of bounded states and clusters of gaps. However, in the case of localized patches, the interaction is always repulsive. In this former case, bounded states of patches are excluded. The analytical formula of the interaction potential is derived and reviewed for both types of interactions and checked by numerical investigation of the model equation.

Explore related subjects

nlin.PS

Keep this discovery

BibTeXRIS

M. Tlidi, E. Berrios-Caro, D. Pinto-Ramo, A. G. Vladimirov, M. Clerc. 2019-12-23. Interaction between localized vegetation patches and gaps in water-limited environments. https://arxiv.org/abs/1912.10875

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Self-similar vector solitons for the coupled higher-order nonlinear Schrodinger equations in inhomogeneous optical fibers

We prove the existence of two kinds of self-similar vector solitons in an inhomogeneous optical fiber medium, where light propagation is governed by a pair of coupled higher-order nonlinear Schrodinger equations with varying second- and third-order dispersions, self- and cross-phase modulation non linearities, self-steepening, and linear gain/loss effects. The newly found self-similar waves comprise bright-W-shaped and kink-antikink waveforms with nonvanishing amplitudes. As a practical exam ple, we discuss the propagation dynamics of these soliton structures in a periodically distributed fiber system as well as an exponential dispersion-decreasing fiber. The results demonstrate that the parameter functions of gain/loss and third-order dispersion serve as a key factor in determining the nonlinear dynamics of self-similar vector solitons. In particular, we find that precise control over the shape and dynamic evolution of self-similar pulses can be achieved through a proper choice of the distributed third-order dispersion parameter, while the gain/loss coefficient controls their intensity.

nlin.PS↗
arXiv2026

Fast Synergetic Simulation to Study Slow Evolution of Soliton Patterns in Optical Resonators

Complex patterns in physical and biological systems often emerge through slow collective dynamics governed by a small number of key variables. In nonlinear optical resonators, dissipative Kerr solitons provide an important example, where interactions between well-separated solitons can evolve over timescales far longer than the characteristic loss and gain timescales. Direct numerical simulation of these dynamics is challenging because stiffness forces conventional methods to resolve many rapidly damped degrees-of-freedom with very small time steps. We present a numerical scheme, the synergetic method, that eliminates these rapidly damped degrees-of-freedom and retains the slowly evolving modes, enabling time steps many orders of magnitude larger than those used in conventional approaches. Applied to soliton molecules in driven Kerr cavities, the method achieves speedups of $10^3$ to $10^5$ while capturing dynamics on laboratory timescales. We use it to model the full interaction dynamics of a three-soliton molecule and the evolution of an eight-soliton molecule. The approach provides an efficient framework for studying slow pattern formation in nonlinear systems with widely separated timescales.

nlin.PS↗
arXiv2026

Breathers in solitonic room-temperature superlattice-induced superfluorescence in quasi-2D perovskites

Recently, a soliton mechanism for room-temperature superfluorescence in thin perovskite films has been proposed, with a fundamental soliton predicted to remain stable under LO phonon--exciton interactions. At the same time, superlattice architectures offer a route to enhancing superfluorescence in perovskites. Motivated by recent observations of room-temperature superfluorescence in periodic superlattices of quasi-2D metal-halide perovskites, we extend the 2D nonlocal nonlinear Schr\"odinger equation describing Wannier exciton--LO phonon interactions to superlattice structures, obtaining a 3D nonlocal nonlinear Schr\"odinger equation. We show that interlayer tunnelling gives rise to breather dynamics corresponding to a stable fundamental soliton in mixed coordinate--momentum space, with the coordinate parallel to the layers and the momentum perpendicular to them. The breather dynamics originate from miniband formation, which induces a momentum-dependent phase modulation of the soliton. In the absence of interlayer tunnelling, the breather dynamics disappear and the soliton becomes stationary. These results establish a direct connection between interlayer tunnelling, miniband formation and soliton dynamics, suggesting that breather behavior can provide a signature of interlayer tunnelling in quasi-2D perovskite superlattices.

nlin.PS↗