Dynamic stability and spatial heterogeneity in the individual-based modelling of a Lotka-Volterra gas

• Autorzy: Waniewski J. , Jędruch W. , Żołek N. S.
• Języki publikacji: EN

Abstrakty

EN

Computer simulation of a few thousands of particles moving (approximately) according to the energy and momentum conservation laws on a tessellation of 800 x 800 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.

Słowa kluczowe

EN

predator-prey system; entropy; correlation coefficient

PL

równanie Lotka-Volterra; entropia; współczynnik korelacji

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2004
• Tom: Vol. 14, no 2
• Strony: 139--147
• Opis fizyczny: Bibliogr.26 poz., rys., tab., wykr.

Twórcy

autor

Waniewski J.

• Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, ul. Trojdena 4, 02–109 Warsaw, Poland; Interdisciplinary Centre for Mathematical and Computational Modelling, Warsaw University, ul. Pawińskiego 5A, 02–106 Warsaw, Poland

autor

Jędruch W.

• Faculty of Electronics, Telecommunications and Informatics, Technical University of Gdańsk, ul. Narutowicza 11/12, 80-952 Gdańsk, Poland

autor

Żołek N. S.

• Institute of Biocybernetics and Biomedical Engineering, Polish Academy of Sciences, ul. Trojdena 4, 02–109 Warsaw, Poland

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