A two-species competition model whose density-dependent growth functions are exponential and rational is analyzed in discrete systems. In this way, changing the geometry of the basin of attraction by changing one of the system’s parameters is discussed and it is shown that changing one of the parameters leads to a sequence of different bifurcation. One of the things that have received the most attention is that the basin of attraction is riddled. The tool with which the riddle conditions of an attractor are examined is the Lyapunov exponent.

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