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The Stationary Coexistence Mechanisms of Biological Communities in the Spaces of Different Dimensions

Student: Anton Savostianov

Supervisor: Alexey Antonovich Nikitin

Faculty: Faculty of Computer Science

Educational Programme: Applied Mathematics and Information Science (Bachelor)

Year of Graduation: 2017

This paper studies two-species model of self-structuring stationary biological communities, proposed by U. Dieckmann and R. Law, applicable for spatially heterogeneous populations. The numerical method applicable for solving the system of integro-differential equations that describes an equilibrium state of the system is developed; number of mathematical heuristics based on Hankel transform in two-dimensional case and Laplace problem with associated Legendre polynomials are proposed; nontrivial stationary points are found; boundaries on the model's parameter space leading to aforementioned nontrivial points are examined. Developed method applied for a number of widely-known biological scenarios.

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