Diffusion Chaos in Reaction – Diffusion Boundary Problem in the Dumbbell Domain
<p>We consider a boundary problem of reaction-diffusion type in the domain consisting of two rectangular areas connected by a bridge. The bridge width is a bifurcation parameter of the problem and is changed in such way that the measure of the domain is preserved. The conditions on chaotic osc...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Yaroslavl State University
2013-01-01
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| Series: | Моделирование и анализ информационных систем |
| Subjects: | |
| Online Access: | http://mais-journal.ru/jour/article/view/194 |
| _version_ | 1797966967568596992 |
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| author | S. D. Glyzin P. L. Shokin |
| author_facet | S. D. Glyzin P. L. Shokin |
| author_sort | S. D. Glyzin |
| collection | DOAJ |
| description | <p>We consider a boundary problem of reaction-diffusion type in the domain consisting of two rectangular areas connected by a bridge. The bridge width is a bifurcation parameter of the problem and is changed in such way that the measure of the domain is preserved. The conditions on chaotic oscillations emergence were studied and the dependence of invariant characteristics of the attractor on the bridge width was constructed. The diffusion parameter was chosen such that in the case of widest possible bridge (corresponding to a rectangular domain) the spatially homogeneous cycle of the problem is orbitally asymptotically stable. By decreasing the bridge width the homogeneous cycle looses stability and then the spatially inhomogeneous chaotic attractor emerges. For the obtained attractor we compute Lyapunov exponents and Lyapunov dimension and notice that the dimension grows as the parameter decreases but is bounded. We show that the dimension growth is connected with the growing complexity of stable solutions distribution with respect to the space variable.</p> |
| first_indexed | 2024-04-11T02:23:43Z |
| format | Article |
| id | doaj.art-68882854058e4f239b423e3cd9a217c0 |
| institution | Directory Open Access Journal |
| issn | 1818-1015 2313-5417 |
| language | English |
| last_indexed | 2024-04-11T02:23:43Z |
| publishDate | 2013-01-01 |
| publisher | Yaroslavl State University |
| record_format | Article |
| series | Моделирование и анализ информационных систем |
| spelling | doaj.art-68882854058e4f239b423e3cd9a217c02023-01-02T23:04:49ZengYaroslavl State UniversityМоделирование и анализ информационных систем1818-10152313-54172013-01-012034357188Diffusion Chaos in Reaction – Diffusion Boundary Problem in the Dumbbell DomainS. D. Glyzin0P. L. Shokin1Ярославский государственный университет им. П.Г. ДемидоваЯрославский государственный университет им. П.Г. Демидова<p>We consider a boundary problem of reaction-diffusion type in the domain consisting of two rectangular areas connected by a bridge. The bridge width is a bifurcation parameter of the problem and is changed in such way that the measure of the domain is preserved. The conditions on chaotic oscillations emergence were studied and the dependence of invariant characteristics of the attractor on the bridge width was constructed. The diffusion parameter was chosen such that in the case of widest possible bridge (corresponding to a rectangular domain) the spatially homogeneous cycle of the problem is orbitally asymptotically stable. By decreasing the bridge width the homogeneous cycle looses stability and then the spatially inhomogeneous chaotic attractor emerges. For the obtained attractor we compute Lyapunov exponents and Lyapunov dimension and notice that the dimension grows as the parameter decreases but is bounded. We show that the dimension growth is connected with the growing complexity of stable solutions distribution with respect to the space variable.</p>http://mais-journal.ru/jour/article/view/194диффузионный хаосаттракторляпуновская размерностьуравнение Гинзбурга – Ландаубифуркация |
| spellingShingle | S. D. Glyzin P. L. Shokin Diffusion Chaos in Reaction – Diffusion Boundary Problem in the Dumbbell Domain Моделирование и анализ информационных систем диффузионный хаос аттрактор ляпуновская размерность уравнение Гинзбурга – Ландау бифуркация |
| title | Diffusion Chaos in Reaction – Diffusion Boundary Problem in the Dumbbell Domain |
| title_full | Diffusion Chaos in Reaction – Diffusion Boundary Problem in the Dumbbell Domain |
| title_fullStr | Diffusion Chaos in Reaction – Diffusion Boundary Problem in the Dumbbell Domain |
| title_full_unstemmed | Diffusion Chaos in Reaction – Diffusion Boundary Problem in the Dumbbell Domain |
| title_short | Diffusion Chaos in Reaction – Diffusion Boundary Problem in the Dumbbell Domain |
| title_sort | diffusion chaos in reaction diffusion boundary problem in the dumbbell domain |
| topic | диффузионный хаос аттрактор ляпуновская размерность уравнение Гинзбурга – Ландау бифуркация |
| url | http://mais-journal.ru/jour/article/view/194 |
| work_keys_str_mv | AT sdglyzin diffusionchaosinreactiondiffusionboundaryprobleminthedumbbelldomain AT plshokin diffusionchaosinreactiondiffusionboundaryprobleminthedumbbelldomain |