Fixed Points of a Mapping Generated by a System of Ordinary Differential Equations with Relay Hysteresis

Standard

Fixed Points of a Mapping Generated by a System of Ordinary Differential Equations with Relay Hysteresis. / Kamachkin, A. M.; Potapov, D. K.; Yevstafyeva, V. V.

In: Differential Equations, Vol. 58, No. 4, 01.04.2022, p. 455-467.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{0d011feb933944739b127fd2a9c91efd,

title = "Fixed Points of a Mapping Generated by a System of Ordinary Differential Equations with Relay Hysteresis",

abstract = "Abstract: We consider an n-dimensional systemof ordinary differential equations with relay hysteresis on the right-hand side. Under certainconditions, the solution of the system defines a self-mapping of bounded sets lying in thediscontinuity surfaces. We obtain conditions for the existence of fixed points of the mapping andthe uniqueness of the fixed point as well as conditions under which fixed points for various types ofmappings exist simultaneously. To each type of mapping there corresponds one type of periodicorbits: either with two switching points (the so-called unimodal orbits) or with an even number ofswitching points greater than two. In the case of unimodal orbits, examples of the existence oforbits of various configurations are given.",

author = "Kamachkin, {A. M.} and Potapov, {D. K.} and Yevstafyeva, {V. V.}",

note = "Publisher Copyright: {\textcopyright} 2022, Pleiades Publishing, Ltd.",

year = "2022",

month = apr,

day = "1",

doi = "10.1134/s0012266122040024",

language = "English",

volume = "58",

pages = "455--467",

journal = "Differential Equations",

issn = "0012-2661",

publisher = "Pleiades Publishing",

number = "4",

}

RIS

TY - JOUR

T1 - Fixed Points of a Mapping Generated by a System of Ordinary Differential Equations with Relay Hysteresis

AU - Kamachkin, A. M.

AU - Potapov, D. K.

AU - Yevstafyeva, V. V.

PY - 2022/4/1

Y1 - 2022/4/1

N2 - Abstract: We consider an n-dimensional systemof ordinary differential equations with relay hysteresis on the right-hand side. Under certainconditions, the solution of the system defines a self-mapping of bounded sets lying in thediscontinuity surfaces. We obtain conditions for the existence of fixed points of the mapping andthe uniqueness of the fixed point as well as conditions under which fixed points for various types ofmappings exist simultaneously. To each type of mapping there corresponds one type of periodicorbits: either with two switching points (the so-called unimodal orbits) or with an even number ofswitching points greater than two. In the case of unimodal orbits, examples of the existence oforbits of various configurations are given.

AB - Abstract: We consider an n-dimensional systemof ordinary differential equations with relay hysteresis on the right-hand side. Under certainconditions, the solution of the system defines a self-mapping of bounded sets lying in thediscontinuity surfaces. We obtain conditions for the existence of fixed points of the mapping andthe uniqueness of the fixed point as well as conditions under which fixed points for various types ofmappings exist simultaneously. To each type of mapping there corresponds one type of periodicorbits: either with two switching points (the so-called unimodal orbits) or with an even number ofswitching points greater than two. In the case of unimodal orbits, examples of the existence oforbits of various configurations are given.

UR - http://www.scopus.com/inward/record.url?scp=85135250656&partnerID=8YFLogxK

U2 - 10.1134/s0012266122040024

DO - 10.1134/s0012266122040024

M3 - Article

AN - SCOPUS:85135250656

VL - 58

SP - 455

EP - 467

JO - Differential Equations

JF - Differential Equations

SN - 0012-2661

IS - 4

ER -

ID: 97770207