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Autovibration in systems with hysteresis. (English. Russian original) Zbl 0715.73026
Sov. Phys., Dokl. 34, No. 12, 1066-1068 (1989); translation from Dokl. Akad. Nauk SSSR 309, No. 5, 1068-1071 (1989).
The discovery of the conditions for the existence of stable cycles and autovibrational modes in nonlinear systems described by differential equations with standard functional nonlinearities is a classical problem of nonlinear mechanics, control theory, and various branches of applied mathematics. The problem of finding analogous conditions for systems with hysteresis nonlinearities (these arise in problems related to plasticity, magnetism, control, and various other branches of mechanics and physics) naturally rises. In this paper we present the results obtained in this field by using the methods developed by the first two authors [Systems with hysteresis (1989; Zbl 0665.47038)]; these treat the hysteresis nonlinearities as transducers with corresponding state spaces and input- state and input-output relations.

MSC:
74J99 Waves in solid mechanics
47J05 Equations involving nonlinear operators (general)
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