On the Existence of Two-Point Oscillatory Solutions of a Perturbed Relay System with Hysteresis

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On the Existence of Two-Point Oscillatory Solutions of a Perturbed Relay System with Hysteresis. / Yevstafyeva, V. V.

In: Differential Equations, Vol. 57, No. 2, 02.2021, p. 155-164.

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

BibTeX

@article{a1c63ccaa14145b8a259133d7bc0b6fc,

title = "On the Existence of Two-Point Oscillatory Solutions of a Perturbed Relay System with Hysteresis",

abstract = "We consider a system of nth-order ordinary differential equations whose right-hand side is the sum of a linear function of the solution with a constant matrix, an essential nonlinearity of the relay type with hysteresis, and a perturbing continuous periodic function. The matrix of the linear function has only real simple nonzero eigenvalues, of which at least one is positive. We study the question of whether such systems have continuous solutions with two switching points in the state space (two-point oscillatory solutions) such that the time in which the solution returns to each of these points coincides with the period of the perturbing function or is an integer fraction of the latter. A sufficient condition for the nonexistence of such solutions is established, and a theorem is proved that gives sufficient conditions for the existence of a two-point oscillatory solution with return time equal to the period of the perturbing function. A corroborating example is given.",

author = "Yevstafyeva, {V. V.}",

year = "2021",

month = feb,

doi = "10.1134/s001226612102004x",

language = "English",

volume = "57",

pages = "155--164",

journal = "Differential Equations",

issn = "0012-2661",

publisher = "Pleiades Publishing",

number = "2",

}

RIS

TY - JOUR

T1 - On the Existence of Two-Point Oscillatory Solutions of a Perturbed Relay System with Hysteresis

AU - Yevstafyeva, V. V.

PY - 2021/2

Y1 - 2021/2

N2 - We consider a system of nth-order ordinary differential equations whose right-hand side is the sum of a linear function of the solution with a constant matrix, an essential nonlinearity of the relay type with hysteresis, and a perturbing continuous periodic function. The matrix of the linear function has only real simple nonzero eigenvalues, of which at least one is positive. We study the question of whether such systems have continuous solutions with two switching points in the state space (two-point oscillatory solutions) such that the time in which the solution returns to each of these points coincides with the period of the perturbing function or is an integer fraction of the latter. A sufficient condition for the nonexistence of such solutions is established, and a theorem is proved that gives sufficient conditions for the existence of a two-point oscillatory solution with return time equal to the period of the perturbing function. A corroborating example is given.

AB - We consider a system of nth-order ordinary differential equations whose right-hand side is the sum of a linear function of the solution with a constant matrix, an essential nonlinearity of the relay type with hysteresis, and a perturbing continuous periodic function. The matrix of the linear function has only real simple nonzero eigenvalues, of which at least one is positive. We study the question of whether such systems have continuous solutions with two switching points in the state space (two-point oscillatory solutions) such that the time in which the solution returns to each of these points coincides with the period of the perturbing function or is an integer fraction of the latter. A sufficient condition for the nonexistence of such solutions is established, and a theorem is proved that gives sufficient conditions for the existence of a two-point oscillatory solution with return time equal to the period of the perturbing function. A corroborating example is given.

UR - http://www.scopus.com/inward/record.url?scp=85102944345&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/9c0c626f-04f6-360c-abba-7796cf487f1b/

U2 - 10.1134/s001226612102004x

DO - 10.1134/s001226612102004x

M3 - Article

AN - SCOPUS:85102944345

VL - 57

SP - 155

EP - 164

JO - Differential Equations

JF - Differential Equations

SN - 0012-2661

IS - 2

ER -

ID: 75471190