Analysis of global bifurcations in a market share attraction model

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Equilibrium selection in a nonlinear duopoly game with adaptive expectations (2001, background): “In order to prove Proposition 1, we need the following Lemma, which is a particular case of a more general statement given in Bischi et al. (2000b) If x > 1 then y < 0 and all the images of higher rank are negative and divergent.”
Three-dimensional discrete-time Lotka-Volterra models with an application to industrial clusters (2010, background): “The choice of discrete time dynamic models is also crucial because they may exhibit more complicated dynamic behaviors.”