Global bifurcation analysis of an adaptive control system (Q1177308)

A simple adaptive control law is shown to lead to the simple two- dimensional system \(\dot x=x-xy+1\), \(\dot y=\mu x^ 2+\nu y\), and the paper deals with the bifurcation analysis of these equations for variations in the parameters \(\mu\), \(\nu\). It is shown that the parameter space \((\nu,\mu)\) can be divided into eight regions and that the system has 13 different topological structures. The global bifurcation analysis of the system is completely determined apart from on the saddle connection curve.