Some Discrete Competition Models and the Competitive Exclusion Principle†

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Monotone maps: A review (2005, background): “[15] who show that is has the same four dynamical outcomes as the classical autonomous Lotka-Volterra ordinary differential equations model of competition.”
Dynamics of a two-dimensional system of rational difference equations of Leslie--Gower type (2011, background): “Special attention to discrete competitive and cooperative systems in the plane was given in [2,3,5-7,10,12,17,20].”
Exclusion and dominance in discrete population models via the carrying simplex (2013, background): “These notions are not new and have been analyzed in [2], [4], [8], [7], [9], [12], [1], [18], [13] and the references therein.”
Rational systems in the plane (2009, unknown): “Consider the system (15, 21): xnþ1 1⁄4 b1xn B1xnþyn ynþ1 1⁄4 a2þg2yn xn 9= ;; n 1⁄4 0; 1; .”