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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:


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

Efimov Anton Viktorovich, Saratov State University
Shabunin Aleksej Vladimirovich, Saratov State University

The in?uence of two types of di?usion 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 di?usion considerably changes 75the 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.

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