A numerical method for determining bifurcation curves of mappings

A shooting type iterative method for determining bifurcation curves of mappings is developed in this paper. By using this method we are able to calculate bifurcation curves for orbits of periods ≤ 5 of a Hénon-like map in all details. We find an interesting phenomenon that two or more stable periodic orbits of the same or different periods may coexist for some combinations of parameter values. Two stable p5 orbits and their attracting regions are shown for (μ, b) = (1.536, 0.153).