On a Special Class of Self-Sustained Oscillations

This paper deals with the “modified van der Pol differential equations” q¨ − (sgn q˙) (δ/2)q˙² h(q) + κ²f(q) = 0, where h(q) and f(q) are suitable functions. It is shown that there exists a unique limit cycle. For the limit amplitude both lower and upper bounds are established in the case of unrestricted values δ. For small values δ the limit amplitude can be calculated immediately.