ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)

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Efimov A. V., Shabunin A. V. Mixing and diffusion effect on spatial-temporal dynamics in stochastic Lotka–Volterra system with discrete phase space. Izvestiya VUZ. Applied Nonlinear Dynamics, 2009, vol. 17, iss. 1, pp. 57-76. DOI: 10.18500/0869-6632-2009-17-1-57-76

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Language: 
Russian
Heading: 
Deterministic Chaos
Article type: 
Article
UDC: 
519.245+517.9+517.39
DOI: 
10.18500/0869-6632-2009-17-1-57-76

Mixing and diffusion effect on spatial-temporal dynamics in stochastic Lotka–Volterra system with discrete phase space

Autors: 
Efimov Anton Viktorovich, Saratov State University
Shabunin Aleksej Vladimirovich, Saratov State University
Abstract: 

The influence of two types of diffusion on dynamics of stochastic lattice Lotka– Volterra model is considered in this work. The simulations were carried out by means of Kinetic Monte-Carlo algorithm. It is shown that the local diffusion considerably changes the dynamics of the model and accelerates the interaction processes on the lattice, while the mixing results in appearance of global periodic oscillations. The global oscillations appear due to phenomenon of phase synchronization. Various characteristics of the system and their dependence on parameters have been considered in detail. Submitted results form the basis for further researches of the control possibilities for systems with competitive dynamics. They also demonstrate one of the plausible reasons of species diversity and stability of population dynamics in ecosystems.

Key words: 
spatial structures
synchronization
self-organization
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Received: 
23.09.2008
Accepted: 
14.01.2009
Published: 
30.04.2009
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