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Theory and Modern Applications

Figure 2 | Advances in Difference Equations

Figure 2

From: Global stability in n-dimensional discrete Lotka-Volterra predator-prey models

Figure 2

Two-dimensional models with ( σ 1 , σ 2 )=(1,1). The dark circles denote initial conditions (see Example 3.10). (a) r 1 a 22 − r 2 a 12 <0 and the limits of the four trajectories are (0, r 2 a 22 )=(0,2). (b)  r 1 a 22 − r 2 a 12 >0. The solutions of equation (3.10) rotate finitely many times around the limit ϑ=(0.455,10.455). (c) r 1 a 22 − r 2 a 12 >0. The solutions of equation (3.10) rotate infinitely many times around the limit ϑ=(0.683,29.317).

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