Impact of Parameter Variability and Environmental Noise on the Klausmeier Model of Vegetation Pattern Formation

Köhnke, Merlin C.; Malchow, Horst

doi:10.3390/math5040069

Cited by 4 publications

(3 citation statements)

References 48 publications

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“…, (5) which is a finite-difference approximation with (possibly) non-homogeneous step h t between x t+1 and x t . Moreover, (5) reduces to (1) when h t = 1, ∀t = 1, .…”

Section: Variability Assessment Of Irregularly Sampled Datamentioning

confidence: 99%

“…Variability, also known as statistical dispersion, scatter, or spread, can be defined as the propensity at which a given signal is likely to change. The analysis of variability is of major importance in many fields, such as astrophysics [1,2], hydrology [3], agriculture [4], or ecology [5,6]. Measuring variability also has important applications in medicine.…”

Section: Introductionmentioning

confidence: 99%

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Assessment of Variability in Irregularly Sampled Time Series: Applications to Mental Healthcare

et al. 2020

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Variability is defined as the propensity at which a given signal is likely to change. There are many choices for measuring variability, and it is not generally known which ones offer better properties. This paper compares different variability metrics applied to irregularly (nonuniformly) sampled time series, which have important clinical applications, particularly in mental healthcare. Using both synthetic and real patient data, we identify the most robust and interpretable variability measures out of a set 21 candidates. Some of these candidates are also proposed in this work based on the absolute slopes of the time series. An additional synthetic data experiment shows that when the complete time series is unknown, as it happens with real data, a non-negligible bias that favors normalized and/or metrics based on the raw observations of the series appears. Therefore, only the results of the synthetic experiments, which have access to the full series, should be used to draw conclusions. Accordingly, the median absolute deviation of the absolute value of the successive slopes of the data is the best way of measuring variability for this kind of time series.

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“…, (5) which is a finite-difference approximation with (possibly) non-homogeneous step h t between x t+1 and x t . Moreover, (5) reduces to (1) when h t = 1, ∀t = 1, .…”

Section: Variability Assessment Of Irregularly Sampled Datamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Assessment of Variability in Irregularly Sampled Time Series: Applications to Mental Healthcare

et al. 2020

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“…A broad range of problems is addressed. The first two papers [1,2] consider some new aspects of the classical problem of pattern formation. The dynamics of infectious diseases is another old problem where many aspects are still poorly understood; this is addressed [3,4].…”

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confidence: 99%

Progress in Mathematical Ecology

Petrovskii

2018

Mathematics

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Turing vegetation patterns in a generalized hyperbolic Klausmeier model

Consolo

Currò

Valenti

2020

Math Methods in App Sciences

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The formation of Turing vegetation patterns in flat arid environments is investigated in the framework of a generalized version of the hyperbolic Klausmeier model. The extensions here considered involve, on the one hand, the strength of the rate at which rainfall water enters into the soil and, on the other hand, the functional dependence of the inertial times on vegetation biomass and soil water. The study aims at elucidating how the inclusion of these generalized quantities affects the onset of bifurcation of supercritical Turing patterns as well as the transient dynamics observed from an uniformly vegetated state towards a patterned state. To achieve these goals, linear and multiple-scales weakly nonlinear stability analysis are addressed, this latter being inspected in both large and small spatial domains. Analytical results are then corroborated by numerical simulations, which also serve to describe more deeply the spatio-temporal evolution of the emerging patterns as well as to characterize the different timescales involved in vegetation dynamics.

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Impact of Parameter Variability and Environmental Noise on the Klausmeier Model of Vegetation Pattern Formation

Cited by 4 publications

References 48 publications

Assessment of Variability in Irregularly Sampled Time Series: Applications to Mental Healthcare

Assessment of Variability in Irregularly Sampled Time Series: Applications to Mental Healthcare

Progress in Mathematical Ecology

Turing vegetation patterns in a generalized hyperbolic Klausmeier model

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