Blue Sky Catastrophe in Systems with Non-classical Relaxation Oscillations
The feasibility of a known blue-sky bifurcation in a class of three-dimensional singularly perturbed systems of ordinary differential equations with one fast and two slow variables is studied. A characteristic property of the considered systems is that they permit so-called nonclassic relaxation osc...
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2015-02-01
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| Series: | Моделирование и анализ информационных систем |
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| Online Access: | https://www.mais-journal.ru/jour/article/view/230 |
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| author | S. D. Glyzin A. Yu. Kolesov N. Kh. Rozov |
| author_facet | S. D. Glyzin A. Yu. Kolesov N. Kh. Rozov |
| author_sort | S. D. Glyzin |
| collection | DOAJ |
| description | The feasibility of a known blue-sky bifurcation in a class of three-dimensional singularly perturbed systems of ordinary differential equations with one fast and two slow variables is studied. A characteristic property of the considered systems is that they permit so-called nonclassic relaxation oscillations, that is, oscillations with slow components asymptotically close to time-discontinuous functions and a δ-like fast component. Cases when blue-sky bifurcation leads to a relaxation cycle or stable two-dimensional torus are analyzed. Also the question of homoclinic structure emergence is considered. |
| format | Article |
| id | doaj-art-e2d59ec992a34811b45a2d9de725e9b5 |
| institution | Matheson Library |
| issn | 1818-1015 2313-5417 |
| language | English |
| publishDate | 2015-02-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj-art-e2d59ec992a34811b45a2d9de725e9b52025-08-04T14:06:40ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172015-02-01221386410.18255/1818-1015-2015-1-38-64223Blue Sky Catastrophe in Systems with Non-classical Relaxation OscillationsS. D. Glyzin0A. Yu. Kolesov1N. Kh. Rozov2P.G. Demidov Yaroslavl State University; Scientific Center in Chernogolovka RASP.G. Demidov Yaroslavl State UniversityM.V. Lomonosov Moscow State UniversityThe feasibility of a known blue-sky bifurcation in a class of three-dimensional singularly perturbed systems of ordinary differential equations with one fast and two slow variables is studied. A characteristic property of the considered systems is that they permit so-called nonclassic relaxation oscillations, that is, oscillations with slow components asymptotically close to time-discontinuous functions and a δ-like fast component. Cases when blue-sky bifurcation leads to a relaxation cycle or stable two-dimensional torus are analyzed. Also the question of homoclinic structure emergence is considered.https://www.mais-journal.ru/jour/article/view/230singularly perturbed systemrelaxation cycleasymptotic behaviorstabilityblue sky catastrophenon-classical relaxation oscillations |
| spellingShingle | S. D. Glyzin A. Yu. Kolesov N. Kh. Rozov Blue Sky Catastrophe in Systems with Non-classical Relaxation Oscillations Моделирование и анализ информационных систем singularly perturbed system relaxation cycle asymptotic behavior stability blue sky catastrophe non-classical relaxation oscillations |
| title | Blue Sky Catastrophe in Systems with Non-classical Relaxation Oscillations |
| title_full | Blue Sky Catastrophe in Systems with Non-classical Relaxation Oscillations |
| title_fullStr | Blue Sky Catastrophe in Systems with Non-classical Relaxation Oscillations |
| title_full_unstemmed | Blue Sky Catastrophe in Systems with Non-classical Relaxation Oscillations |
| title_short | Blue Sky Catastrophe in Systems with Non-classical Relaxation Oscillations |
| title_sort | blue sky catastrophe in systems with non classical relaxation oscillations |
| topic | singularly perturbed system relaxation cycle asymptotic behavior stability blue sky catastrophe non-classical relaxation oscillations |
| url | https://www.mais-journal.ru/jour/article/view/230 |
| work_keys_str_mv | AT sdglyzin blueskycatastropheinsystemswithnonclassicalrelaxationoscillations AT ayukolesov blueskycatastropheinsystemswithnonclassicalrelaxationoscillations AT nkhrozov blueskycatastropheinsystemswithnonclassicalrelaxationoscillations |