Abstract
We consider a competition system between two-species containing riddled basin and second basin attractors. To characterize local geometry of riddled basin, we compute a global stability index for the attractor in the system. Our results show that the index varies from \(\infty \) down to positive values within a parameter region. The changes of the index indicates that the attractor looses its stability from asymptotically stable attractor to riddled basin attractor. Thus, the stability index has a great potential to become a new study on bifurcation of dynamical system since it is able to characterize different types of geometry of basins of attraction.
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