Global Stability Boundaries and Hidden Oscillations in Dynamical Models with Dry Friction

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Global Stability Boundaries and Hidden Oscillations in Dynamical Models with Dry Friction. / Kuznetsov, Nikolay V.; Akimova, Elizaveta D.; Kudryashova, Elena V.; Kuznetsova, Olga A.; Lobachev, Mikhail Y.; Mokaev, Ruslan N.; Mokaev, Timur N.

Advanced Structured Materials. Springer Nature, 2022. p. 387-411 (Advanced Structured Materials; Vol. 164).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › Research › peer-review

BibTeX

@inbook{852fda06910b4672a2d4a56ce2a88dae,

title = "Global Stability Boundaries and Hidden Oscillations in Dynamical Models with Dry Friction",

abstract = "In this chapter, the issues of global stability, bifurcations, and emergence of nontrivial limiting dynamic regimes in systems described by differential equations with discontinuous right-hand sides are considered within the framework of the theory of hidden oscillations. Such systems are important in the problems of mechanics, engineering, and control, and arise both a priori and as a result of idealization of some characteristics included in real physical systems. Determining the boundaries of global stability, scenarios of its violation, as well as identifying all arising limiting oscillations are the key challenges in the design of real systems based on mathematical modeling. While the self-excitation of oscillations can be effectively investigated numerically, the identification of hidden oscillations requires special analytical and numerical methods. The analysis of hidden oscillations is necessary to determine the exact boundaries of global stability, to estimate the gap between the necessary and sufficient conditions of global stability, and their convergence. This work presents a number of theoretical results and engineering problems in which hidden oscillations (their absence or presence and location) play an important role.",

keywords = "Control theory, Differential inclusions, Global stability, Hidden attractors, Periodic oscillations, Theory of hidden oscillations",

author = "Kuznetsov, {Nikolay V.} and Akimova, {Elizaveta D.} and Kudryashova, {Elena V.} and Kuznetsova, {Olga A.} and Lobachev, {Mikhail Y.} and Mokaev, {Ruslan N.} and Mokaev, {Timur N.}",

note = "Publisher Copyright: {\textcopyright} 2022, The Author(s), under exclusive license to Springer Nature Switzerland AG.",

year = "2022",

month = jan,

day = "1",

doi = "10.1007/978-3-030-93076-9_20",

language = "English",

series = "Advanced Structured Materials",

publisher = "Springer Nature",

pages = "387--411",

booktitle = "Advanced Structured Materials",

address = "Germany",

}

RIS

TY - CHAP

T1 - Global Stability Boundaries and Hidden Oscillations in Dynamical Models with Dry Friction

AU - Kuznetsov, Nikolay V.

AU - Akimova, Elizaveta D.

AU - Kudryashova, Elena V.

AU - Kuznetsova, Olga A.

AU - Lobachev, Mikhail Y.

AU - Mokaev, Ruslan N.

AU - Mokaev, Timur N.

PY - 2022/1/1

Y1 - 2022/1/1

N2 - In this chapter, the issues of global stability, bifurcations, and emergence of nontrivial limiting dynamic regimes in systems described by differential equations with discontinuous right-hand sides are considered within the framework of the theory of hidden oscillations. Such systems are important in the problems of mechanics, engineering, and control, and arise both a priori and as a result of idealization of some characteristics included in real physical systems. Determining the boundaries of global stability, scenarios of its violation, as well as identifying all arising limiting oscillations are the key challenges in the design of real systems based on mathematical modeling. While the self-excitation of oscillations can be effectively investigated numerically, the identification of hidden oscillations requires special analytical and numerical methods. The analysis of hidden oscillations is necessary to determine the exact boundaries of global stability, to estimate the gap between the necessary and sufficient conditions of global stability, and their convergence. This work presents a number of theoretical results and engineering problems in which hidden oscillations (their absence or presence and location) play an important role.

AB - In this chapter, the issues of global stability, bifurcations, and emergence of nontrivial limiting dynamic regimes in systems described by differential equations with discontinuous right-hand sides are considered within the framework of the theory of hidden oscillations. Such systems are important in the problems of mechanics, engineering, and control, and arise both a priori and as a result of idealization of some characteristics included in real physical systems. Determining the boundaries of global stability, scenarios of its violation, as well as identifying all arising limiting oscillations are the key challenges in the design of real systems based on mathematical modeling. While the self-excitation of oscillations can be effectively investigated numerically, the identification of hidden oscillations requires special analytical and numerical methods. The analysis of hidden oscillations is necessary to determine the exact boundaries of global stability, to estimate the gap between the necessary and sufficient conditions of global stability, and their convergence. This work presents a number of theoretical results and engineering problems in which hidden oscillations (their absence or presence and location) play an important role.

KW - Control theory

KW - Differential inclusions

KW - Global stability

KW - Hidden attractors

KW - Periodic oscillations

KW - Theory of hidden oscillations

UR - http://www.scopus.com/inward/record.url?scp=85128983561&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/b1b4c548-fca8-396d-b945-cbe81c68ab49/

U2 - 10.1007/978-3-030-93076-9_20

DO - 10.1007/978-3-030-93076-9_20

M3 - Chapter

AN - SCOPUS:85128983561

T3 - Advanced Structured Materials

SP - 387

EP - 411

BT - Advanced Structured Materials

PB - Springer Nature

ER -

ID: 95230411