Spatial dynamics of a vegetation model in an arid flat environment

Sun, Gui‐Quan; Li, Li; Zhang, Zi-Ke

doi:10.1007/s11071-013-0935-3

Cited by 38 publications

(21 citation statements)

References 38 publications

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“…Furthermore, based on the standard multiple scale analysis [73][74][75][76][77][78], whereby a model solution is constructed using a series expansion in terms of a small independent variable (see Appendix A.2 for details), it is possible to exactly delineate the regions of the phase space in which different patterns arise. As illustrated in Fig.…”

Section: Transitions Between Stationary Patternsmentioning

confidence: 99%

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Pattern transitions in spatial epidemics: Mechanisms and emergent properties

Sun

Jusup

Jin

et al. 2016

Physics of Life Reviews

Self Cite

236

115

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Infectious diseases are a threat to human health and a hindrance to societal development. Consequently, the spread of diseases in both time and space has been widely studied, revealing the different types of spatial patterns. Transitions between patterns are an emergent property in spatial epidemics that can serve as a potential trend indicator of disease spread. Despite the usefulness of such an indicator, attempts to systematize the topic of pattern transitions have been few and far between. We present a mini-review on pattern transitions in spatial epidemics, describing the types of transitions and their underlying mechanisms. We show that pattern transitions relate to the complexity of spatial epidemics by, for example, being accompanied with phenomena such as coherence resonance and cyclic evolution. The results presented herein provide valuable insights into disease prevention and control, and may even be applicable outside epidemiology, including other branches of medical science, ecology, quantitative finance, and elsewhere.

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Section: Transitions Between Stationary Patternsmentioning

confidence: 99%

“…A stationary pattern seen in the spatial distribution of a disease implies a stable state regardless of the initial conditions [77,78,143]. Such a state is usually accompanied by areas in which the density of the disease is high and hence difficult to get rid off.…”

Section: Early Warnings For the Outbreak Of Infectious Diseasesmentioning

confidence: 99%

Pattern transitions in spatial epidemics: Mechanisms and emergent properties

Sun

Jusup

Jin

et al. 2016

Physics of Life Reviews

Self Cite

236

115

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show abstract

“…By comparing the results from Figs. 3,4,5,6,7,8,9,10, and 11 and the results from Figs. 12, 13, 14, 15, 16, and 17, it confirms that collapse (or jump shift) in parameter a, c makes the ordered state give different responses because the distribution and regularity of the network depend on the parameters in different degrees.…”

Section: Diffusion Of the Emergence Of Damagementioning

confidence: 81%

“…regular spatial patterns due to internal competition and collaboration, or under appropriate external forcing as well [1][2][3][4][5][6][7][8][9][10][11][12]. In ecological systems, species enjoy their lives by improving its adaption to circumstance.…”

mentioning

confidence: 99%

Prediction for breakup of spiral wave in a regular neuronal network

Ren

et al. 2015

Nonlinear Dyn

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Target wave and spiral wave can regulate the collective behaviors of electrical activities in neuronal systems as a powerful 'pacemaker'. Disordered states occur when normal signal propagation among neurons is disturbed and neuronal disease could be induced. In this paper, a stable rotating spiral wave is developed as initial state that the two-dimensional neuronal network of Hindmarsh-Rose neuron shows distinct periodicity and regularity in space, and then, some parameters are changed sharply to model the destruction effect induced by external large forcing or internal collapse, and the destructed areas will be expanded to occupy a larger area by expanding the damaged boundary in random way. The collapse and instability of spiral wave, ordered states could be predicated by monitoring and analyzing the time series of some nodes. It could be useful to detect the emergence of disaster in some biological or ecological systems.

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“…In the vicinity of the bifurcation point (such as the Turing and Hopf bifurcations) the critical amplitude A j (j = 1, 2, 3) follows the general form, and its standard form can be derived by standard technically analysis and symmetry breaking theory [9][10][11]. Normal forms of the critical amplitude can be well applied to the study of pattern formation and the subtle changes of the pattern formation are derived through appropriately spatial symmetry terms [12].…”

Section: Introductionmentioning

confidence: 99%

Dynamics of an epidemic model with spatial diffusion

Wang

2014

Physica A: Statistical Mechanics and its Applications

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h i g h l i g h t s• We obtained a spatial epidemic model with logistic growth. • Using multiple-scale analysis, we present amplitude equations. • There are different types of stationary patterns. • Reaction diffusion epidemic systems have rich dynamics. a b s t r a c tMathematical models are very useful in analyzing the spread and control of infectious diseases which can be used to predict the developing tendency of the infectious disease, determine the key factors and to seek the optimum strategies of disease control. As a result, we investigated the pattern dynamics of a spatial epidemic model with logistic growth. By using amplitude equation, we found that there were different types of stationary patterns including spotted, mixed, and stripe patterns, which mean that spatial motion of individuals can form high density of diseases. The obtained results can be extended in other related fields, such as vegetation patterns in ecosystems.

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Spatial dynamics of a vegetation model in an arid flat environment

Cited by 38 publications

References 38 publications

Pattern transitions in spatial epidemics: Mechanisms and emergent properties

Pattern transitions in spatial epidemics: Mechanisms and emergent properties

Prediction for breakup of spiral wave in a regular neuronal network

Dynamics of an epidemic model with spatial diffusion

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