On Natural Continua of Periodic Solutions of the Systems with Hysteresis

Abstract

Theorems on the existence of continua of periodic solutions for systems with hysteretic nonlinearities of the type of Preisah models are suggested. It is found that in the general situation, the standard criteria for existence of at least one periodic solution, which rest on the use of prior upper-bound estimates of 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.