Bifurcation and Global Dynamics of a Leslie-Gower Type Competitive System of Rational Difference Equations with Quadratic Terms

Figure 2

Equilibria in different parameter regions for the number of equilibria of system (1) when , , , and are fixed positive real numbers, as given by Proposition 11. Each circle in the parameters -plane indicates the existence of an isolated equilibrium point of system (1) in the nonnegative quadrant of the -plane. Local stability character of equilibria as given in Theorem 19 is indicated as follows: , locally asymptotically stable equilibrium; ⊖, saddle; ◯, repelling equilibrium point: two-colored circle, semistable nonhyperbolic equilibrium.