Multiple limit cycle bifurcation surfaces and global families of multiple limit cycles
``Sufficient conditions are given for the local existence of multiplicity-\(m\) limit cycle bifurcation surfaces, \(C_m\), of planar analytic systems depending on \(n\) parameters with \(n \geq m \geq 2\). In the generic case, the surfaces \(C_2\), \(C_3\), and \(C_4\) are the familiar saddle-node, cusp, and swallow-tail bifurcation surfaces, respectively. The author's termination principle for global one-parameter families of simple limit cycles of relatively prime, planar, analytic systems is generalized to a termination principle for global one- parameter families of multiple limit cycles which implies that the boundary of a global limit cycle bifurcation surface typically consists of Hopf bifurcation surfaces and/or homoclinic (or heteroclinic) loop bifurcation surfaces''.
scientific article; zbMATH DE number 810064