Deterministic Limits to Stochastic Spatial Models of Natural Enemies

2002 ◽  
Vol 159 (1) ◽  
pp. 57-80 ◽  
Author(s):  
M. J. Keeling ◽  
H. B. Wilson ◽  
S. W. Pacala
Keyword(s):  
Natural Enemies ◽  
Spatial Models ◽  
Stochastic Spatial Models

Deterministic Limits to Stochastic Spatial Models of Natural Enemies

2002 ◽  
Vol 159 (1) ◽  
pp. 57
Author(s):  
Keeling ◽  
Wilson ◽  
Pacala
Keyword(s):  
Natural Enemies ◽  
Spatial Models ◽  
Stochastic Spatial Models

scholarly journals Stochastic Spatial Models

SIAM Review ◽  
1999 ◽  
Vol 41 (4) ◽  
pp. 677-718 ◽  
Author(s):  
Rick Durrett
Keyword(s):  
Spatial Models ◽  
Stochastic Spatial Models

Stochastic Spatial Models: A User's Guide to Ecological Applications

1994 ◽  
Vol 343 (1305) ◽  
pp. 329-350 ◽  
Author(s):  
Richard Durrett ◽  
Simon A. Levin
Keyword(s):  
Interacting Particle Systems ◽  
Spatial Models ◽  
Simulation Models ◽  
Ecological Interactions ◽  
Stochastic Effects ◽  
Interacting Particle ◽  
Stochastic Spatial Models ◽  
Non Local ◽  
Discrete Analogues ◽  
Mathematical Literature

Spatial pattern, how it arises and how it is maintained, are central foci for ecological theory. In recent years, some attention has shifted from continuum models to spatially discrete analogues, which allow easy treatment of local stochastic effects and of non-local spatial influences. Many of these fall within the area of mathematics known as `interacting particle systems', which provides a body of results that facilitate the interpretation of the suite of simulation models that have been considered, and point towards future analyses. In this paper we review the basic mathematical literature. Three influential examples from the ecological literature are considered and placed within the general framework, which is shown to be a powerful one for the study of spatial ecological interactions.

scholarly journals Stochastic Spatial Models in Ecology: A Statistical Physics Approach

2017 ◽  
Vol 172 (1) ◽  
pp. 44-73 ◽  
Author(s):  
Simone Pigolotti ◽  
Massimo Cencini ◽  
Daniel Molina ◽  
Miguel A. Muñoz
Keyword(s):  
Statistical Physics ◽  
Spatial Models ◽  
Stochastic Spatial Models

A NUMERICAL STUDY ON PREDATOR PREY MODEL

2012 ◽  
Vol 09 ◽  
pp. 347-353
Author(s):  
MOHAMED FARIS LAHAM ◽  
ISTHRINAYAGY KRISHNARAJAH ◽  
ABDUL KADIR JUMAAT
Keyword(s):  
Stochastic Processes ◽  
Numerical Study ◽  
Spatial Models ◽  
Euler Method ◽  
Volterra Model ◽  
Population Cycle ◽  
Stochastic Representation ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Stochastic Spatial Models

Stochastic spatial models are becoming a popular tool for understand the ecological and evolution of ecosystem problems. We consider the predator prey interactions in term of stochastic representation of this Lotka-Volterra model and explore the use of stochastic processes to extinction behavior of the interacting populations. Here, we present simulation of stochastic processes of continuous time Lotka-Volterra model. Euler method has been used to solve the predator prey system. The trajectory spiral graph has been plotted based on obtained solution to show the population cycle of predator as a function of time.

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