ABSTRACT
This chapter introduces the main notions for rather simple bifurcations. In particular, the so-called codimension-one bifurcations of equilibrium points will be dealt with. The term codimension-one refers to the fact that the occurrence of the bifurcation depends on a single parameter. Codimension-one bifurcations are introduced with first-order models, which are the simplest dynamical systems exhibiting such phenomena, but are relevant also for higher-order systems. The normal form of a bifurcation is very important as it represents the elementary system showing the given bifurcation and, at the same time, the core mechanism in higher-order systems affected by the same bifurcation. The shape of the diagram explains the origin of the name subcritical pitchfork bifurcation. Saddle-node bifurcation type of bifurcation is characterized by a mechanism that leads to create, collapse, and annihilate equilibrium points. In the transcritical bifurcation the equilibrium points always persist, but when the bifurcation point is crossed they exchange their stability properties.
