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

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
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