INVESTIGATION OF OSCILLATORY SOLUTIONS OF DIFFERENTIAL-DIFFERENCE EQUATIONS OF SECOND ORDER IN A CRITICAL CASE
We consider a differential-difference equation of second order of delay type, containing the delay of the function and its derivatives. Such equations occur in the modeling of electronic devices. The nature of the loss of the zero solution stability is studied. The possibility of stability loss rela...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2015-06-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/261 |
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| author | E. P. Kubyshkin A. R. Moryakova |
| author_facet | E. P. Kubyshkin A. R. Moryakova |
| author_sort | E. P. Kubyshkin |
| collection | DOAJ |
| description | We consider a differential-difference equation of second order of delay type, containing the delay of the function and its derivatives. Such equations occur in the modeling of electronic devices. The nature of the loss of the zero solution stability is studied. The possibility of stability loss related to the passing of two pairs of purely imaginary roots, that are in resonance 1:3, through an imaginary axis is shown. In this case bifurcating oscillatory solutions are studied. It is noted the existence of a chaotic attractor for which Lyapunov exponents and Lyapunov dimension are calculated. As an investigation techniques we use the theory of integral manifolds and normal forms method for nonlinear differential equations. |
| format | Article |
| id | doaj-art-d91d33d9ba4446e5b73497d703cf7195 |
| institution | Kabale University |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2015-06-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-d91d33d9ba4446e5b73497d703cf71952025-08-20T03:44:18ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172015-06-0122343944710.18255/1818-1015-2015-3-439-447250INVESTIGATION OF OSCILLATORY SOLUTIONS OF DIFFERENTIAL-DIFFERENCE EQUATIONS OF SECOND ORDER IN A CRITICAL CASEE. P. Kubyshkin0A. R. Moryakova1P.G. Demidov Yaroslavl State UniversityP.G. Demidov Yaroslavl State UniversityWe consider a differential-difference equation of second order of delay type, containing the delay of the function and its derivatives. Such equations occur in the modeling of electronic devices. The nature of the loss of the zero solution stability is studied. The possibility of stability loss related to the passing of two pairs of purely imaginary roots, that are in resonance 1:3, through an imaginary axis is shown. In this case bifurcating oscillatory solutions are studied. It is noted the existence of a chaotic attractor for which Lyapunov exponents and Lyapunov dimension are calculated. As an investigation techniques we use the theory of integral manifolds and normal forms method for nonlinear differential equations.https://www.mais-journal.ru/jour/article/view/261: d-splittingmethod of integral manifoldsbifurcation theorychaotic oscillations |
| spellingShingle | E. P. Kubyshkin A. R. Moryakova INVESTIGATION OF OSCILLATORY SOLUTIONS OF DIFFERENTIAL-DIFFERENCE EQUATIONS OF SECOND ORDER IN A CRITICAL CASE Моделирование и анализ информационных систем : d-splitting method of integral manifolds bifurcation theory chaotic oscillations |
| title | INVESTIGATION OF OSCILLATORY SOLUTIONS OF DIFFERENTIAL-DIFFERENCE EQUATIONS OF SECOND ORDER IN A CRITICAL CASE |
| title_full | INVESTIGATION OF OSCILLATORY SOLUTIONS OF DIFFERENTIAL-DIFFERENCE EQUATIONS OF SECOND ORDER IN A CRITICAL CASE |
| title_fullStr | INVESTIGATION OF OSCILLATORY SOLUTIONS OF DIFFERENTIAL-DIFFERENCE EQUATIONS OF SECOND ORDER IN A CRITICAL CASE |
| title_full_unstemmed | INVESTIGATION OF OSCILLATORY SOLUTIONS OF DIFFERENTIAL-DIFFERENCE EQUATIONS OF SECOND ORDER IN A CRITICAL CASE |
| title_short | INVESTIGATION OF OSCILLATORY SOLUTIONS OF DIFFERENTIAL-DIFFERENCE EQUATIONS OF SECOND ORDER IN A CRITICAL CASE |
| title_sort | investigation of oscillatory solutions of differential difference equations of second order in a critical case |
| topic | : d-splitting method of integral manifolds bifurcation theory chaotic oscillations |
| url | https://www.mais-journal.ru/jour/article/view/261 |
| work_keys_str_mv | AT epkubyshkin investigationofoscillatorysolutionsofdifferentialdifferenceequationsofsecondorderinacriticalcase AT armoryakova investigationofoscillatorysolutionsofdifferentialdifferenceequationsofsecondorderinacriticalcase |