Related papers: A Numerical Bifurcation Analysis of a Dryland Vege…
We study the mechanisms of pattern formation for vegetation dynamics in water-limited regions. Our analysis is based on a set of two partial differential equations (PDEs) of reaction-diffusion type for the biomass and water and one ordinary…
A feature common to many models of vegetation pattern formation in semi-arid ecosystems is a sequence of qualitatively different patterned states, "gaps -> labyrinth -> spots", that occurs as a parameter representing precipitation…
A particular sequence of patterns, "$\text{gaps} \to \text{labyrinth} \to \text{spots}$," occurs with decreasing precipitation in previously reported numerical simulations of PDE dryland vegetation models. These observations have led to the…
The original Hardenberg's model of biomass patterns in arid and semi-arid regions is revisited to extend it to more general non flat regions. It is proposed a technique to study these more generalized (non-flat) regions using both a…
This paper delves into a systematically reduced plant system proposed by Ja\"ibi et al. [Phys. D, 2020] in arid area. They used the method of geometric singular perturbation to study the existence of abundant orbits. Instead, we deliberate…
We present a modified water-vegetation model to investigate the mechanistic relationship between infiltration-soil moisture feedback and vegetation pattern in arid/semi-arid ecosystems. Employing Turing pattern formation theory, we drive…
A cross-diffusion system modeling the information herding of individuals is analyzed in a bounded domain with no-flux boundary conditions. The variables are the species' density and an influence function which modifies the information state…
A model of the dynamics of natural rotifer populations is described as a discrete nonlinear map depending on three parameters, which reflect characteristics of the population and environment. Model dynamics and their change by variation of…
Localised radial patterns have been observed in the vegetation of semi-arid ecosystems, often as localised patches of vegetation or in the form of `fairy circles'. We consider stationary localised radial solutions to a reduced model for…
Bifurcation theory is the usual analytic approach to study the parameter space of a dynamical system. Despite the great power of prediction of these techniques, fundamental limitations appear during the study of a given problem. Nonlinear…
We perform both analytical and numerical bifurcation analysis of a forest-grassland ecosystem model coupled with human interaction. The model consists of two nonlinear ordinary differential equations incorporating the human perception of…
Localised patterns are often observed in models for dryland vegetation, both as peaks of vegetation in a desert state and as gaps within a vegetated state, known as `fairy circles'. Recent results from radial spatial dynamics show that…
In many drylands around the globe, vegetation self-organizes into regular spatial patterns in response to aridity stress. We consider the regularly-spaced vegetation bands, on gentle hill-slopes, that survive low rainfall conditions by…
In order to investigate the evolutionary process of many deterministic Dynamical systems with unfixed parameter, a set of dynamical models with parameter changing continuously and the accumulation of this change might be large is introduced…
Drylands are pattern-forming systems showing self-organized vegetation patchiness, multiplicity of stable states and fronts separating domains of alternative stable states. Pattern dynamics, induced by droughts or disturbances, can result…
We propose a model of multispecies populations surviving on distributed resources. System dynamics are investigated under changes in abiotic factors such as the climate, as parameterized through environmental temperature. In particular, we…
We develop a model for investigating the impact of rainstorm variability on the formation of banded vegetation patterns in dryland ecosystems. Water input, during rare rainstorms, is modeled as an instantaneous kick to the soil water. The…
In this paper we consider the 2-component reaction-diffusion model that was recently obtained by a systematic reduction of the 3-component Gilad et al. model for dryland ecosystem dynamics. The nonlinear structure of this model is more…
We investigate the bifurcation structure of equilibria in a class of non-autonomous ordinary differential equations governed by a season length parameter, $\tau$, which determines the alternation between growth and decline dynamics. This…
The climate is a complex non-equilibrium dynamical system that relaxes toward a steady state under the continuous input of solar radiation and dissipative mechanisms. The steady state is not necessarily unique. A useful tool to describe the…