Rachinskii, Dmitrii Asymptotic stability of large-amplitude oscillations in systems with hysteresis. (English) Zbl 0938.34036 NoDEA, Nonlinear Differ. Equ. Appl. 6, No. 3, 267-288 (1999). The system under investigation is \[ dz/dt= A(t; \lambda)z+ f(t, n(t);\lambda),\quad z\in\mathbb{R}^N, \] where \(\lambda\) is a parameter, \(A(t,\lambda)\) is a square matrix of order \(N\), and \(n(t)\) is the defined output of a hysteresis nonlinearity. Several theorems on the number, localization and asymptotic stability of large-amplitude periodic solutions to the system are proved. Reviewer: P.Smith (Keele) Cited in 3 Documents MSC: 34C25 Periodic solutions to ordinary differential equations 34D20 Stability of solutions to ordinary differential equations 34C55 Hysteresis for ordinary differential equations Keywords:oscillations; stability; hysteresis; large-amplitude periodic solutions PDF BibTeX XML Cite \textit{D. Rachinskii}, NoDEA, Nonlinear Differ. Equ. Appl. 6, No. 3, 267--288 (1999; Zbl 0938.34036) Full Text: DOI