NUMERICAL STUDY OF COEXISTENCE OF POPULATIONS IN AN ENVIRONMENTAL NICHE
Abstract
The predator-prey interactions on the spatial heterogeneous two-dimensional area are described. The model is written as a system of nonlinear parabolic equations for two closely related predator populations and two prey populations competing for the general resource. It is shown that under certain relationships between the parameters and the variable natural habitat resource functions, the model belongs to the class of the cosymmetric dynamical systems. In this case, there is a continuous family of stationary distributions of the coexistent populations. The simulation experiment is based on the method of straight lines, and on the scheme of staggered grids. The balance method is used for the approximation in spatial variables of the task on a rectangular area. The results showing the model capabilities for describing the formation of the population stationary distributions are presented. The formation of the biological structures is studied under the growth parameter heterogeneity; the conditions for the coexistence of closely related types are analyzed.
Supporting agencies: The research is done with the financial support from RFFI (grant no. 14-01-00470)
About the Authors
Alexander Vladimirovich Budyanskiy
Don State Technical University, Russia
Russian Federation
Russian Federation
Mikhail Gennadyevich Kruglikov
Southern Federal University, Russia
Russian Federation
Russian Federation
Vyacheslav Georgiyevich Tsybulin
Southern Federal University, Russia
Russian Federation
Russian Federation
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Review
For citations:
Budyanskiy A.V., Kruglikov M.G., Tsybulin V.G. NUMERICAL STUDY OF COEXISTENCE OF POPULATIONS IN AN ENVIRONMENTAL NICHE. Vestnik of Don State Technical University. 2014;14(2):28-35. (In Russ.) https://doi.org/10.12737/4475
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