Stationary distribution of a stochastic vegetation–water system with reaction–diffusion

2022 ◽  
Vol 123 ◽  
pp. 107589
Author(s):  
Shiliang Pan ◽  
Qimin Zhang ◽  
Anke Meyer-Baese
Keyword(s):  
Stationary Distribution ◽  
Water System ◽  
Reaction Diffusion ◽  
Vegetation Water

Near‐optimal control of a stochastic vegetation‐water system with reaction diffusion

2020 ◽  
Vol 43 (9) ◽  
pp. 6043-6061
Author(s):  
Shiliang Pan ◽  
Qimin Zhang ◽  
Meyer‐Baese Anke
Keyword(s):  
Optimal Control ◽  
Water System ◽  
Reaction Diffusion ◽  
Vegetation Water

scholarly journals Finite-time stability and optimal control of an impulsive stochastic reaction-diffusion vegetation-water system driven by L$ {\rm \acute{e}} $vy process with time-varying delay

2021 ◽  
Vol 18 (6) ◽  
pp. 8462-8498
Author(s):  
Zixiao Xiong ◽  
◽  
Xining Li ◽  
Ming Ye ◽  
Qimin Zhang ◽  
...  
Keyword(s):  
Optimal Control ◽  
Finite Time ◽  
Water System ◽  
Reaction Diffusion ◽  
Time Varying ◽  
Time Stability ◽  
Finite Time Stability ◽  
Time Varying Delay ◽  
Vegetation Water ◽  
Varying Delay

<abstract><p>In this paper, a reaction-diffusion vegetation-water system with time-varying delay, impulse and L$ {\rm \acute{e}} $vy jump is proposed. The existence and uniqueness of the positive solution are proved. Meanwhile, mainly through the principle of comparison, we obtain the sufficient conditions for finite-time stability which reflect the effect of time delay, diffusion, impulse, and noise. Besides, considering the planting, irrigation and other measures, we introduce control variable into the vegetation-water system. In order to save the costs of strategies, the optimal control is analyzed by using the minimum principle. Finally, numerical simulations are shown to illustrate the effectiveness of our theoretical results.</p></abstract>

scholarly journals The influence of autotoxicity on the dynamics of vegetation spots

2020 ◽  
Author(s):  
Annalisa Iuorio ◽  
Frits Veerman
Keyword(s):  
Dynamical System ◽  
Reaction Diffusion ◽  
Homoclinic Orbits ◽  
Spatial Dimension ◽  
Travelling Wave ◽  
Singular Perturbation Theory ◽  
Geometric Singular Perturbation Theory ◽  
Scaling Analysis ◽  
Water Models ◽  
Vegetation Water

AbstractPlant autotoxicity has proved to play an essential role in the behaviour of local vegetation. We analyse a reaction-diffusion-ODE model describing the interactions between vegetation, water, and autotoxicity. The presence of autotoxicity is seen to induce movement and deformation of spot patterns in some parameter regimes, a phenomenon which does not occur in classical biomass-water models. We aim to analytically quantify this novel feature, by studying travelling wave solutions in one spatial dimension. We use geometric singular perturbation theory to prove the existence of symmetric, stationary and non-symmetric, travelling pulse solutions, by constructing appropriate homoclinic orbits in the associated 5-dimensional dynamical system. In the singularly perturbed context, we perform an extensive scaling analysis of the dynamical system, identifying multiple asymptotic scaling regimes where (travelling) pulses may or may not be constructed. We discuss the agreement and discrepancy between the analytical results and numerical simulations. Our findings indicate how the inclusion of an additional ODE may significantly influence the properties of classical biomass-water models of Klausmeier/Gray–Scott type.

Normal approximations to discrete unimodal distributions

1986 ◽  
Vol 23 (04) ◽  
pp. 1013-1018
Author(s):  
B. G. Quinn ◽  
H. L. MacGillivray
Keyword(s):  
Stationary Distribution ◽  
Sufficient Conditions ◽  
Random Variables ◽  
Hypergeometric Distribution ◽  
Death Process ◽  
Normal Approximations ◽  
Discrete Random Variables ◽  
Birth Death

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.

Surface reactions observed by photoemission electron microscopy (PEEM)

1992 ◽  
Vol 50 (1) ◽  
pp. 286-287
Author(s):  
H.H. Rotermund
Keyword(s):  
Electron Microscopy ◽  
Electron Microscope ◽  
Work Function ◽  
Chemical Reactions ◽  
Reaction Diffusion ◽  
Dynamic Processes ◽  
Clean Surface ◽  
Crystal Surfaces ◽  
Single Crystal Surfaces ◽  
Photoemission Electron

Chemical reactions at a surface will in most cases show a measurable influence on the work function of the clean surface. This change of the work function δφ can be used to image the local distributions of the investigated reaction,.if one of the reacting partners is adsorbed at the surface in form of islands of sufficient size (Δ>0.2μm). These can than be visualized via a photoemission electron microscope (PEEM). Changes of φ as low as 2 meV give already a change in the total intensity of a PEEM picture. To achieve reasonable contrast for an image several 10 meV of δφ are needed. Dynamic processes as surface diffusion of CO or O on single crystal surfaces as well as reaction / diffusion fronts have been observed in real time and space.

Vesicles as an equilibrium structure of a simple surfactant-water system

1994 ◽  
Vol 4 (9) ◽  
pp. 1585-1604 ◽  
Author(s):  
L. Cantù ◽  
M. Corti ◽  
E. Del Favero ◽  
A. Raudino
Keyword(s):  
Water System ◽  
Equilibrium Structure
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