Dynamic stability and spatial heterogeneityin the individualbased modelling of a lotkavolterra gas

Jacek Waniewski; Wojciech Jędruch; Norbert Żołek

International Journal of Applied Mathematics and Computer Science (2004)

  • Volume: 14, Issue: 2, page 139-147
  • ISSN: 1641-876X

Abstract

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Computer simulation of a few thousands of particles moving (approximately) according to the energy and momentum conservation laws on a tessellation of squares in discrete time steps and interacting according to the predator-prey scheme is analyzed. The population dynamics are described by the basic Lotka-Volterra interactions (multiplication of preys, predation and multiplication of predators, death of predators), but the spatial effects result in differences between the system evolution and the mathematical description by the Lotka-Volterra equations. The spatial patterns were evaluated using entropy and a cross correlation coefficient for the spatial distribution of both populations. In some simulations the system oscillated with variable amplitude but rather stable period, but the particle distribution departed from the (quasi) homogeneous state and did not return to it. The distribution entropy oscillated in the same rhythm as the population, but its value was smaller than in the initial homogeneous state. The cross correlation coefficient oscillated between positive and negative values. Its average value depended on the space scale applied for its evaluation with the negative values on the small scale (separation of preys from predators) and the positive values on the large scale (aggregation of both populations). The stability of such oscillation patterns was based on a balance of the population parameters and particle mobility. The increased mobility (particle mixing) resulted in unstable oscillations with high amplitude, sustained homogeneity of the particle distribution, and final extinction of one or both populations.

How to cite

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Waniewski, Jacek, Jędruch, Wojciech, and Żołek, Norbert. "Dynamic stability and spatial heterogeneityin the individualbased modelling of a lotkavolterra gas." International Journal of Applied Mathematics and Computer Science 14.2 (2004): 139-147. <http://eudml.org/doc/207685>.

@article{Waniewski2004,
abstract = {Computer simulation of a few thousands of particles moving (approximately) according to the energy and momentum conservation laws on a tessellation of squares in discrete time steps and interacting according to the predator-prey scheme is analyzed. The population dynamics are described by the basic Lotka-Volterra interactions (multiplication of preys, predation and multiplication of predators, death of predators), but the spatial effects result in differences between the system evolution and the mathematical description by the Lotka-Volterra equations. The spatial patterns were evaluated using entropy and a cross correlation coefficient for the spatial distribution of both populations. In some simulations the system oscillated with variable amplitude but rather stable period, but the particle distribution departed from the (quasi) homogeneous state and did not return to it. The distribution entropy oscillated in the same rhythm as the population, but its value was smaller than in the initial homogeneous state. The cross correlation coefficient oscillated between positive and negative values. Its average value depended on the space scale applied for its evaluation with the negative values on the small scale (separation of preys from predators) and the positive values on the large scale (aggregation of both populations). The stability of such oscillation patterns was based on a balance of the population parameters and particle mobility. The increased mobility (particle mixing) resulted in unstable oscillations with high amplitude, sustained homogeneity of the particle distribution, and final extinction of one or both populations.},
author = {Waniewski, Jacek, Jędruch, Wojciech, Żołek, Norbert},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {entropy; correlation coefficient; predator-prey system},
language = {eng},
number = {2},
pages = {139-147},
title = {Dynamic stability and spatial heterogeneityin the individualbased modelling of a lotkavolterra gas},
url = {http://eudml.org/doc/207685},
volume = {14},
year = {2004},
}

TY - JOUR
AU - Waniewski, Jacek
AU - Jędruch, Wojciech
AU - Żołek, Norbert
TI - Dynamic stability and spatial heterogeneityin the individualbased modelling of a lotkavolterra gas
JO - International Journal of Applied Mathematics and Computer Science
PY - 2004
VL - 14
IS - 2
SP - 139
EP - 147
AB - Computer simulation of a few thousands of particles moving (approximately) according to the energy and momentum conservation laws on a tessellation of squares in discrete time steps and interacting according to the predator-prey scheme is analyzed. The population dynamics are described by the basic Lotka-Volterra interactions (multiplication of preys, predation and multiplication of predators, death of predators), but the spatial effects result in differences between the system evolution and the mathematical description by the Lotka-Volterra equations. The spatial patterns were evaluated using entropy and a cross correlation coefficient for the spatial distribution of both populations. In some simulations the system oscillated with variable amplitude but rather stable period, but the particle distribution departed from the (quasi) homogeneous state and did not return to it. The distribution entropy oscillated in the same rhythm as the population, but its value was smaller than in the initial homogeneous state. The cross correlation coefficient oscillated between positive and negative values. Its average value depended on the space scale applied for its evaluation with the negative values on the small scale (separation of preys from predators) and the positive values on the large scale (aggregation of both populations). The stability of such oscillation patterns was based on a balance of the population parameters and particle mobility. The increased mobility (particle mixing) resulted in unstable oscillations with high amplitude, sustained homogeneity of the particle distribution, and final extinction of one or both populations.
LA - eng
KW - entropy; correlation coefficient; predator-prey system
UR - http://eudml.org/doc/207685
ER -

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