On natural continua of periodic solutions of the systems with hysteresis. (English. Russian original) Zbl 1071.34045

Rachinskij, D. I.

Autom. Remote Control 64, No. 3, 420-438 (2003); translation from Avtom. Telemekh. 2003, No. 3, 84-103 (2003).

Summary: Theorems on the existence of continua of periodic solutions for systems with hysteretic nonlinearities of the type of Preisach models are suggested. It is found that in general situation, the standard criteria for the existence of at least one periodic solution, which rest on the use of prior upper-bound estimates on the norm of periodic solutions and the Leray-Schauder method, ensure the existence of a one-parameter continuum of periodic solutions to these systems. The proofs are based on the use of new classes of operators that describe periodic responses of hysteretic nonlinearities to periodic inputs.

MSC:

34C55	Hysteresis for ordinary differential equations
34C25	Periodic solutions to ordinary differential equations

Keywords:

Preisach model