Bifurcation theorems and limit cycles in nonlinear systems—I.

Abstract

Two bifurcation theorems are established concerning the qualitative change in the integral curves of the hard-excitation type nonlinear systems at a point of bifurcation (or a branch point) where different regions meet. Two classes of this type (Type B) are considered. These exhibit limit cycles which do not contract to the origin, unlike the soft-excitation type nonlinear systems (Type A) reported by Jonnada and Weygandt. A Type B, Class 1, system is exemplified by the well-known van der Pol equation. A third-order example (B-1 system) is also given. Type B, Class 2 systems exhibit an unstable limit cycle. Second- and third-order examples are given for B-2 systems.