Bifurcations

Many dynamical systems depend on parameters. One may expect that small variations of the parameters produce no significant changes in the orbits. As was shown in Chap. 3 for the Logistic Map, even in simple cases, there exist critical values such that, moving the parameters through them, the orbits can change dramatically. In the present chapter, we first provide the definition of homoclinic and heteroclinic orbits and then a summary about local bifurcations for both the continuous case and the discrete-time case. Global bifurcations will be presented in the next following chapter.