Asymptotic stability of large-amplitude oscillations in systems with hysteresis. (English) Zbl 0938.34036

Rachinskii, Dmitrii

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)

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