Linear stability analysis of systems with Preisach memory. (English) Zbl 1181.47075

Pimenov, Alexander; Rachinskii, Dmitrii

Discrete Contin. Dyn. Syst., Ser. B 11, No. 4, 997-1018 (2009).

The authors consider differential equations with the Preisach operator or its generalizations providing the non-local memory effects characterized by the rate independence and the permanent effect of shocks. Some algorithms for the linearisation of the evolution operator of the system are proposed and, finally, some examples of the applicability of the system in terrestrial hydrology and for electronic oscillators with hysteresis are presented.

Reviewer: Leszek Gasiński (Kraków)

MSC:

47J40	Equations with nonlinear hysteresis operators
34C25	Periodic solutions to ordinary differential equations
86A05	Hydrology, hydrography, oceanography
47N99	Miscellaneous applications of operator theory

Keywords:

periodic solution; operator-differential equation; local stability analysis; Preisach model