DYNAMICS OF COMPOSITIONS OF LOTKA–VOLTERRA OPERATORS FOR SOME PARTIALLY ORIENTED GRAPHS IN A THREE-DIMENSIONAL SIMPLEX
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This article studies the dynamics of compositions of Lotka–Volterra operators for some partially directed graphs in a three-dimensional simplex. The study analyzes the stability of population interaction models for different graph structures and their spatial dynamic properties. Using nonlinear differential equations, limit states and equilibrium points of iterative processes for Lotka–Volterra systems are determined, and types of asymptotic behavior between them are described. The role of operator compositions in relation to invariant sets and their importance as mathematical models are also shown. The results obtained serve to better understand the evolutionary stability of population systems and the influence of graph structure on their dynamics.
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