On a bifurcation governed by hysteresis nonlinearity |
| |
Authors: | Alexander Krasnosel'skii Dmitrii Rachinskii |
| |
Affiliation: | (1) Institute for Information Transmission Problems, Russian Academy of Sciences, Bol'shoi Karetnyi per. 19, Moscow 101447, Russia, e-mail: amk@iitp.ru, RU |
| |
Abstract: | We consider autonomous systems with a nonlinear part depending on a parameter and study Hopf bifurcations at infinity. The nonlinear part consists of the nonlinear functional term and the Prandtl--Ishlinskii hysteresis term. The linear part of the system has a special form such that the close-loop system can be considered as a hysteresis perturbation of a quasilinear Hamiltonian system. The Hamiltonian system has a continuum of arbitrarily large cycles for each value of the parameter. We present sufficient conditions for the existence of bifurcation points for the non-Hamiltonian system with hysteresis. These bifurcation points are determined by simple characteristics of the hysteresis nonlinearity. |
| |
Keywords: | : Hopf bifurcation at infinity large cycles hysteresis operators control theory equation. |
本文献已被 SpringerLink 等数据库收录! |