Two-cycles of the Ricker model with the periodic Malthusian parameter: stability and multistability

This paper investigates the emergence and stability of 2-cycles for the Ricker model with the 2-year periodic Malthusian parameter. It is shown that the stability loss of the trivial solution occurs through the transcritical bifurcation resulting in a stable 2-cycle. The subsequent tangent bifurcation leads to the appearance of two new 2-cycles: stable and unstable ones. As a result, there is multistability. It is shown that the coexistence of two different stable 2-cycles is possible in a narrow area of the parameter space. Further stability loss of the 2-cycles occurs according to the Feigenbaum scenario.