Local Stability in 3D Discrete Dynamical Systems: Application to a Ricker Competition Model

Figure 3

The stability regions and the bifurcation scenario of the two-dimensional Ricker competition model (31), in the parameter space , when the competition parameters and are fixed such that . The region is the stability region of the coexistence equilibrium point , the region is the stability region of the exclusion fixed point , and the region is the stability region of the exclusion fixed point . A period-doubling bifurcation scenario occurs (in the coexistence case) as we cross from region to region , from region to region , and so on. Similarly, one has a period-doubling scenario (in the exclusion case) in the -axis as we cross from region to region , from region to region , and so on. Similar phenomenon occurs in regions , for .