Non-stationary delay of nonlinear oscillations of a magnetoelastic system under conditions of external excitation and initial magnetization offset

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The phenomenon of non-stationary delay in excitation of high-amplitude chaotic oscillations in a system of two coupled oscillators is considered. A brief description of two real physical systems that allow excitation of chaotic oscillations with non-stationary delay is given. It is shown that oscillations in both systems can be de-scribed based on the same model of two coupled oscillators, one of which is non-linear and the other is linear. A system of two second-order differential equations is given for such a model. This system is simplified while preserving the kernel that provides the effect of delay in high-amplitude chaotic oscillations. The possibility of replacing external excitation in the system with the initial displacement of one of the oscillators is considered.

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Sobre autores

A. Ivanov

Pitirim Sorokin Syktyvkar State University

Autor responsável pela correspondência
Email: alivaht@mail.ru
Rússia, Oktyabr’skii prosp., 55, Syktyvkar, Komi Republic, 167001

V. Shavrov

Kotel’nikov Institute of Radio Engineering and Electronics RAS

Email: alivaht@mail.ru
Rússia, Mokhovaya Str., 11, build. 7, Moscow, 125009

V. Shcheglov

Kotel’nikov Institute of Radio Engineering and Electronics RAS

Email: alivaht@mail.ru
Rússia, Mokhovaya Str., 11, build. 7, Moscow, 125009

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2. Fig. 1. Development of oscillations in time, derivatives of the displacement, and parametric portraits of the first oscillator in the cases of external excitation (left column) and initial displacement (right column). Constructions (a), (c), (d) correspond to the solution of system (3)–(4), and constructions (b), (d), (e) – to the solution of system (6)–(7). Parameters of constructions (a), (c), (e): ω1 = 5; ω2 = 15; β1 = 1; β2 = 0.1; γ1 = 10; γ2 = 10; δ = 5; η = −200; A = 70; ω0 = 5; x10 = x20 = 0; . Parameters of constructions (b), (d), (e): ω1 = 5; ω2 = 15; β1 = 0; β2 = 0; γ1 = 10; γ2 = 10; δ = 5; η = −200; A = 0; ω0 – arbitrary; x10 = 2.16; x20 = 0;.

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3. Fig. 2. Development of oscillations in time, derivatives of the displacement, and parametric portraits of the second oscillator in the cases of external excitation (left column) and initial displacement (right column). Constructions (a), (c), (d) correspond to the solution of system (3)–(4), and constructions (b), (d), (e) – to the solution of system (6)–(7). Parameters of constructions (a), (c), (e): ω1 = 5; ω2 = 15; β1 = 1; β2 = 0.1; γ1 = 10; γ2 = 10; δ = 5; η = −200; A = 70; ω0 = 5; x10 = x20 = 0; . Parameters of constructions (b), (d), (e): ω1 = 5; ω2 = 15; β1 = 0; β2 = 0; γ1 = 10; γ2 = 10; δ = 5; η = −200; A = 0; ω0 – arbitrary; x10 = 2.16; x20 = 0;.

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