Limit cycle function of the second kind for autonomous systems on the cylinder (Q647675)

Consider two-dimensional autonomous systems \[ {du\over dt}= P(u,y),\qquad {dy\over dt}= Q(u,y)\tag{\(*\)} \] with \(P,Q\in C^1(\mathbb{R}^2,\mathbb{R})\), and \(P\), \(Q\) \(2\pi\)-periodic in the first variable. Thus, the phase space of \((*)\) can be identified with the cylinder \(Z:= S^1\times\mathbb{R}\). In case that \(P\) and \(Q\) are not periodic in any phase variable, the authors developed tools to estimate the number of limit cycles of \((*)\) and their location, namely the generalized Dulac function and the limit cycle function (Andronov-Hopf function). Their goal in the present paper is to extend these approaches to a cylindric phase space in order to study limit cycles of the second kind (cannot shrink to a point). Special emphasis is paid to constructive methods (using linear programming).