A correlation between the Fukuma-Matsubara and circle criteria for the determination of jump resonance

Jump resonance is a particular type of discontinuity, the absence of which may be predicted by using one form of the circle criterion. Another method of determining presence or absence of jump resonance is due to Fukuma and Matsubara [1]. These two methods are compared after rederiving the Fukuma-Matsubara criterion using different bounds on the nonlinearity. The Fukuma-Matsubara criterion is found to yield a critical region inside the critical circle. Furthermore, an example is given in which the Fukuma-Matsubara criterion predicts the gain needed to produce jump resonance.