Dynamic analysis of a plant-water model with spatial diffusion

Sun, Gui‐Quan; Zhang, Hongtao; Song, Yongli; Li, Li; Jin, Zhen

doi:10.1016/j.jde.2022.05.009

Cited by 56 publications

(13 citation statements)

References 68 publications

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“…where M represents density-independent mortality and J is the yield of plant biomass from uptaken water. This classical model was later analysed, modified, and extended in different aspects (e.g., [28][29][30][31][32][33][34][35][36][37]). In the case of flat terrains, the gradient term in (1) can be replaced with a second diffusion term with a different diffusion constant.…”

Section: Introductionmentioning

confidence: 99%

Delay Effects on Plant Stability and Symmetry-Breaking Pattern Formation in a Klausmeier-Gray-Scott Model of Semiarid Vegetation

Medjahdi,

Lachachi,

Castro

et al. 2024

Symmetry

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The Klausmeier–Gray–Scott model of vegetation dynamics consists of a system of two partial differential equations relating plant growth and soil water. It is capable of reproducing the characteristic spatial patterns of vegetation found in plant ecosystems under water limitations. Recently, a discrete delay was incorporated into this model to account for the lag between water infiltration into the soil and the following water uptake by plants. In this work, we consider a more ecologically realistic distributed delay to relate plant growth and soil water availability and analyse the effects of different delay types on the dynamics of both mean-field and spatial Klausmeier–Gray–Scott models. We consider distributed delays based on Gamma kernels and use the so-called linear chain trick to analyse the stability of the uniformly vegetated equilibrium. It is shown that the presence of delays can lead to the loss of stability in the constant equilibrium and to a reduction of the parameter region where steady-state vegetation patterns can arise through symmetry-breaking by diffusion-driven instability. However, these effects depend on the type of delay, and they are absent for distributed delays with weak kernels when vegetation mortality is low.

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Section: Introductionmentioning

confidence: 99%

Delay Effects on Plant Stability and Symmetry-Breaking Pattern Formation in a Klausmeier-Gray-Scott Model of Semiarid Vegetation

Medjahdi,

Lachachi,

Castro

et al. 2024

Symmetry

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show abstract

“…The research showed that the pattern trend changes gradually in the spatially expanded ecosystem [16]. Moreover, other scholars have also established relevant systems to study vegetation patterns [17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Rich dynamics of a vegetation–water system with the hydrotropism effect

Wang

Hou

2023

Front. Phys.

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In recent years, with the abnormal global climate change, the problem of desertification has become more and more serious. The vegetation pattern is accompanied by desertification, and thus, the study of the vegetation pattern is helpful to better understand the causes of desertification. In this work, we reveal the influences of hydrotropism on the vegetation pattern based on a vegetation–water system in the form of reaction–diffusion equations. Parameter ranges for the steady-state mode obtained by analyzing the system show the dynamic behavior near the bifurcation point. Furthermore, we found that vegetation hydrotropism not only induces spatial pattern generation but also promotes the growth of vegetation itself in this area. Therefore, through the study of vegetation patterns, we can take corresponding preventive measures to effectively prevent land desertification and improve the stability of the ecosystem in the region.

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“…For the convenience of investigating practical systems, they are usually modeled as complex networks, such as biology, ecology, physics and medicine [1][2][3][4][5][6][7][8]. The abbreviated complex network usually consists of nodes and edges which represent individuals and connections among individuals, respectively.…”

Section: Introductionmentioning

confidence: 99%

An effective method for epidemic suppression by edge removing in complex network

Liang

Cui²,

Zhu³

2023

Front. Phys.

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Since the birth of human beings, the spreading of epidemics such as COVID-19 affects our lives heavily and the related studies have become hot topics. All the countries are trying to develop effective prevention and control measures. As a discipline that can simulate the transmission process, complex networks have been applied to epidemic suppression, in which the common approaches are designed to remove the important edges and nodes for controlling the spread of infection. However, the naive removal of nodes and edges in the complex network of the epidemic would be practically infeasible or incur huge costs. With the focus on the effect of epidemic suppression, the existing methods ignore the network connectivity, leading to two serious problems. On the one hand, when we remove nodes, the edges connected to the nodes are also removed, which makes the node is isolated and the connectivity is quickly reduced. On the other hand, although removing edges is less detrimental to network connectivity than removing nodes, existing methods still cause great damage to the network performance in reality. Here, we propose a method to measure edge importance that can protect network connectivity while suppressing epidemic. In the real-world, our method can not only lower the government’s spending on epidemic suppression but also persist the economic growth and protect the livelihood of the people to some extent. The proposed method promises to be an effective tool to maintain the functionality of networks while controlling the spread of diseases, for example, diseases spread through contact networks.

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Dynamic analysis of a plant-water model with spatial diffusion

Cited by 56 publications

References 68 publications

Delay Effects on Plant Stability and Symmetry-Breaking Pattern Formation in a Klausmeier-Gray-Scott Model of Semiarid Vegetation

Delay Effects on Plant Stability and Symmetry-Breaking Pattern Formation in a Klausmeier-Gray-Scott Model of Semiarid Vegetation

Rich dynamics of a vegetation–water system with the hydrotropism effect

An effective method for epidemic suppression by edge removing in complex network

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