TY - JOUR
T1 - Asymptotic stability of continuum sets of periodic solutions to systems with hysteresis
AU - Brokate, M.
AU - Pokrovskii, A.
AU - Rachinskii, D.
N1 - Funding Information:
* Corresponding author. Fax: +353 21 4270813. E-mail addresses: [email protected] (M. Brokate), [email protected] (A. Pokrovskii), [email protected] (D. Rachinskii). 1 This work was initiated during the research stay of D. Rachinskii at the Technical University Munich supported by the research fellowship from the Alexander von Humboldt Foundation. His work was partially supported by the Russian Science Support Foundation, Russian Foundation for Basic Research (Grants 03-01-00258, 04-01-00330), and Grants of the President of Russia (Grants MD-87.2003.01, NS-1532.2003.1). The support is gratefully acknowledged.
PY - 2006/7/1
Y1 - 2006/7/1
N2 - We consider hysteresis perturbations of a system of ODEs which possesses an asymptotically stable periodic solution z*. Where the oscillation of an appropriate projection of this periodic solution is smaller than some threshold number defined by the hysteresis nonlinearity, it is shown that the perturbed system has a continuum of periodic solutions with a rather simple structure in a vicinity of z*. The main result is a theorem on the stability of this continuum.
AB - We consider hysteresis perturbations of a system of ODEs which possesses an asymptotically stable periodic solution z*. Where the oscillation of an appropriate projection of this periodic solution is smaller than some threshold number defined by the hysteresis nonlinearity, it is shown that the perturbed system has a continuum of periodic solutions with a rather simple structure in a vicinity of z*. The main result is a theorem on the stability of this continuum.
KW - Hysteresis perturbations of ODE
KW - Periodic solutions
KW - Preisach hysteresis nonlinearity
KW - Stability
UR - http://www.scopus.com/inward/record.url?scp=33645537624&partnerID=8YFLogxK
U2 - 10.1016/j.jmaa.2006.02.060
DO - 10.1016/j.jmaa.2006.02.060
M3 - Article
AN - SCOPUS:33645537624
SN - 0022-247X
VL - 319
SP - 94
EP - 109
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 1
ER -