Global bifurcation analysis of an adaptive control system

Abstract

The authors present a complete bifurcation analysis of a two-parameter, two-dimensional quadratic ODE (ordinary differential equation) which arises in the study of model reference adaptive control systems. The 2-D ODE exhibits saddle-node, (subcritical) Hopf, and saddle-loop bifurcations. The authors are able to describe the bifurcation diagram completely by identifying all the bifurcation curves. All but the saddle-loop bifurcation curves are explicitly characterized. The saddle-loop bifurcation curve, however, is described qualitatively, and its endpoints as well as its relative position are identified.<>