Hierarchical modeling of nonlinear multivariate spatio-temporal dynamical systems in the presence of uncertainty

2012 ◽  
Author(s):  
William B. Leeds
Keyword(s):  
Dynamical Systems ◽  
Hierarchical Modeling ◽  
Spatio Temporal

scholarly journals Assessing the Spatial and Spatio-Temporal Distribution of Forest Species via Bayesian Hierarchical Modeling

Forests ◽  
2018 ◽  
Vol 9 (9) ◽  
pp. 573 ◽  
Author(s):  
Óscar Rodríguez de Rivera ◽  
Antonio López-Quílez ◽  
Marta Blangiardo
Keyword(s):  
Hierarchical Modeling ◽  
Temporal Distribution ◽  
Short Term ◽  
Distribution Models ◽  
Address Climate Change ◽  
Bayesian Hierarchical ◽  
Temporal Models ◽  
Spatio Temporal ◽  
The Relationship

Climatic change is expected to affect forest development in the short term, as well as the spatial distribution of species in the long term. Species distribution models are potentially useful tools for guiding species choices in reforestation and forest management prescriptions to address climate change. The aim of this study is to build spatial and spatio-temporal models to predict the distribution of four different species present in the Spanish Forest Inventory. We have compared the different models and showed how accounting for dependencies in space and time affect the relationship between species and environmental variables.

scholarly journals Spatio-temporal patterns with hyperchaotic dynamics in diffusively coupled biochemical oscillators

1997 ◽  
Vol 1 (2) ◽  
pp. 161-167 ◽  
Author(s):  
Gerold Baier ◽  
Sven Sahle
Keyword(s):  
Dynamical Systems ◽  
Finite Number ◽  
Temporal Patterns ◽  
Autocatalytic Reaction ◽  
Living Systems ◽  
First Order ◽  
Autocatalytic Reactions ◽  
Complex Patterns ◽  
Spatio Temporal

We present three examples how complex spatio-temporal patterns can be linked to hyperchaotic attractors in dynamical systems consisting of nonlinear biochemical oscillators coupled linearly with diffusion terms. The systems involved are: (a) a two-variable oscillator with two consecutive autocatalytic reactions derived from the Lotka–Volterra scheme; (b) a minimal two-variable oscillator with one first-order autocatalytic reaction; (c) a three-variable oscillator with first-order feedback lacking autocatalysis. The dynamics of a finite number of coupled biochemical oscillators may account for complex patterns in compartmentalized living systems like cells or tissue, and may be tested experimentally in coupled microreactors.

Dynamical Systems Based Spatio-Temporal EEG/MEG Modeling

NeuroImage ◽  
1998 ◽  
Vol 7 (4) ◽  
pp. S675
Author(s):  
C. Uhl ◽  
F. Kruggel ◽  
D.Y. von Cramon
Keyword(s):  
Dynamical Systems ◽  
Spatio Temporal

Controlling Chaos with Parametric Perturbations

1998 ◽  
Vol 08 (08) ◽  
pp. 1693-1698 ◽  
Author(s):  
Leone Fronzoni ◽  
Michele Giocondo
Keyword(s):  
Dynamical System ◽  
Liquid Crystal ◽  
Dynamical Systems ◽  
Electronic Device ◽  
Parametric Perturbation ◽  
Mechanical Device ◽  
Controlling Chaos ◽  
Onset Of Chaos ◽  
Spatio Temporal ◽  
Suppression Of Chaos

We consider the effects of parametric perturbation on the onset of chaos in different dynamical systems. Favoring or suppression of chaos was observed depending on the phase or the frequency of the periodic perturbation. A lowering of the threshold of chaos was observed in an electronic device simulating a Josephson-Junction model and the suppression of chaos was obtained in a bistable mechanical device. We showed that in case of spatial instability in a sample of liquid crystal, the action of the parametric perturbation is to modify the velocity and the onset of the defects. Considering that the emergence of defects precedes the threshold of spatio-temporal chaos, we infer that parametric perturbation can modify the threshold of chaos in this spatial dynamical system.

OSCILLATIONS ON THE EDGE OF CHAOS VIA DISSIPATION AND DIFFUSION

2007 ◽  
Vol 17 (05) ◽  
pp. 1531-1573 ◽  
Author(s):  
MAKOTO ITOH ◽  
LEON O. CHUA
Keyword(s):  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Reaction Diffusion ◽  
Coupled System ◽  
Reaction Diffusion Equations ◽  
Nonlinear Dynamical ◽  
Edge Of Chaos ◽  
Secondary Purpose ◽  
Spatio Temporal ◽  
And Diffusion

The primary purpose of this paper is to show that simple dissipation can bring about oscillations in certain kinds of asymptotically stable nonlinear dynamical systems; namely when the system is locally active where the dissipation is introduced. Furthermore, if these nonlinear dynamical systems are coupled with appropriate choice of diffusion coefficients, then the coupled system can exhibit spatio-temporal oscillations. The secondary purpose of this paper is to show that spatio-temporal oscillations can occur in spatially discrete reaction diffusion equations operating on the edge of chaos, provided the array size is sufficiently large.

Spatial Statistics

2018 ◽  
Author(s):  
Christopher K. Wikle
Keyword(s):  
Machine Learning ◽  
Spatial Statistics ◽  
Spatial Data ◽  
Point Processes ◽  
Hierarchical Modeling ◽  
Climate Science ◽  
Spatial Process ◽  
Wide Range ◽  
Spatio Temporal ◽  
Specific Implementation

The climate system consists of interactions between physical, biological, chemical, and human processes across a wide range of spatial and temporal scales. Characterizing the behavior of components of this system is crucial for scientists and decision makers. There is substantial uncertainty associated with observations of this system as well as our understanding of various system components and their interaction. Thus, inference and prediction in climate science should accommodate uncertainty in order to facilitate the decision-making process. Statistical science is designed to provide the tools to perform inference and prediction in the presence of uncertainty. In particular, the field of spatial statistics considers inference and prediction for uncertain processes that exhibit dependence in space and/or time. Traditionally, this is done descriptively through the characterization of the first two moments of the process, one expressing the mean structure and one accounting for dependence through covariability.Historically, there are three primary areas of methodological development in spatial statistics: geostatistics, which considers processes that vary continuously over space; areal or lattice processes, which considers processes that are defined on a countable discrete domain (e.g., political units); and, spatial point patterns (or point processes), which consider the locations of events in space to be a random process. All of these methods have been used in the climate sciences, but the most prominent has been the geostatistical methodology. This methodology was simultaneously discovered in geology and in meteorology and provides a way to do optimal prediction (interpolation) in space and can facilitate parameter inference for spatial data. These methods rely strongly on Gaussian process theory, which is increasingly of interest in machine learning. These methods are common in the spatial statistics literature, but much development is still being done in the area to accommodate more complex processes and “big data” applications. Newer approaches are based on restricting models to neighbor-based representations or reformulating the random spatial process in terms of a basis expansion. There are many computational and flexibility advantages to these approaches, depending on the specific implementation. Complexity is also increasingly being accommodated through the use of the hierarchical modeling paradigm, which provides a probabilistically consistent way to decompose the data, process, and parameters corresponding to the spatial or spatio-temporal process.Perhaps the biggest challenge in modern applications of spatial and spatio-temporal statistics is to develop methods that are flexible yet can account for the complex dependencies between and across processes, account for uncertainty in all aspects of the problem, and still be computationally tractable. These are daunting challenges, yet it is a very active area of research, and new solutions are constantly being developed. New methods are also being rapidly developed in the machine learning community, and these methods are increasingly more applicable to dependent processes. The interaction and cross-fertilization between the machine learning and spatial statistics community is growing, which will likely lead to a new generation of spatial statistical methods that are applicable to climate science.

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