Energy redistribution in hierarchical systems of oscillators
The article deals with the mathematical model for media with hierarchical structure. Using the hamiltonian formalism, the dynamical system describing the state of hierarchically connected structural elements was derived. According to the analysis of the Poincar\'e sections, we found the localiz...
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| creator | Danylenko, V. A Mykulyak, S. V Skurativskyi, S. I |
| description | The article deals with the mathematical model for media with hierarchical
structure. Using the hamiltonian formalism, the dynamical system describing the
state of hierarchically connected structural elements was derived. According to
the analysis of the Poincar\'e sections, we found the localized quasi-periodic
and chaotic trajectories in the three-level hierarchical model. Moreover,
studies of correlation functions shown that the power spectrum for three-level
model possesses local maxima characterizing temporal scales with strong
correlation. Using the Fourier analysis of the solution's components, we have
studied the distribution of energy injected in the system over hierarchical
levels. Dynamical phenomena in the multi-level system were studied as well. |
| doi_str_mv | 10.48550/arxiv.1503.05759 |
| format | Article |
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structure. Using the hamiltonian formalism, the dynamical system describing the
state of hierarchically connected structural elements was derived. According to
the analysis of the Poincar\'e sections, we found the localized quasi-periodic
and chaotic trajectories in the three-level hierarchical model. Moreover,
studies of correlation functions shown that the power spectrum for three-level
model possesses local maxima characterizing temporal scales with strong
correlation. Using the Fourier analysis of the solution's components, we have
studied the distribution of energy injected in the system over hierarchical
levels. Dynamical phenomena in the multi-level system were studied as well.</description><identifier>DOI: 10.48550/arxiv.1503.05759</identifier><language>eng</language><subject>Physics - Chaotic Dynamics</subject><creationdate>2015-03</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,780,885</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/1503.05759$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.1503.05759$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Danylenko, V. A</creatorcontrib><creatorcontrib>Mykulyak, S. V</creatorcontrib><creatorcontrib>Skurativskyi, S. I</creatorcontrib><title>Energy redistribution in hierarchical systems of oscillators</title><description>The article deals with the mathematical model for media with hierarchical
structure. Using the hamiltonian formalism, the dynamical system describing the
state of hierarchically connected structural elements was derived. According to
the analysis of the Poincar\'e sections, we found the localized quasi-periodic
and chaotic trajectories in the three-level hierarchical model. Moreover,
studies of correlation functions shown that the power spectrum for three-level
model possesses local maxima characterizing temporal scales with strong
correlation. Using the Fourier analysis of the solution's components, we have
studied the distribution of energy injected in the system over hierarchical
levels. Dynamical phenomena in the multi-level system were studied as well.</description><subject>Physics - Chaotic Dynamics</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2015</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj8tOwzAQAH3hgFo-gBP-gQQ79mZtqRdUlYdUqZfeo427ppbSBNkBkb9HFE5zG80Ica9VbR2AeqT8nb5qDcrUChD8rdjsRs7vi8x8SmXOqf-c0zTKNMpz4kw5nFOgQZalzHwpcopyKiENA81TLmtxE2kofPfPlTg-747b12p_eHnbPu0ratFXLdlGRY2R4OR7zdYbCkgIEMhBg8EyYxNNa1vbN-zZ6d4ZYtQWQUdnVuLhT3vN7z5yulBeut-N7rphfgByyEMj</recordid><startdate>20150319</startdate><enddate>20150319</enddate><creator>Danylenko, V. A</creator><creator>Mykulyak, S. V</creator><creator>Skurativskyi, S. I</creator><scope>ALA</scope><scope>GOX</scope></search><sort><creationdate>20150319</creationdate><title>Energy redistribution in hierarchical systems of oscillators</title><author>Danylenko, V. A ; Mykulyak, S. V ; Skurativskyi, S. I</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a679-6a420f17fa5d9b1e493ac7a755ca8527c4ee72f36464b2e9e81b83ae714751f83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2015</creationdate><topic>Physics - Chaotic Dynamics</topic><toplevel>online_resources</toplevel><creatorcontrib>Danylenko, V. A</creatorcontrib><creatorcontrib>Mykulyak, S. V</creatorcontrib><creatorcontrib>Skurativskyi, S. I</creatorcontrib><collection>arXiv Nonlinear Science</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Danylenko, V. A</au><au>Mykulyak, S. V</au><au>Skurativskyi, S. I</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Energy redistribution in hierarchical systems of oscillators</atitle><date>2015-03-19</date><risdate>2015</risdate><abstract>The article deals with the mathematical model for media with hierarchical
structure. Using the hamiltonian formalism, the dynamical system describing the
state of hierarchically connected structural elements was derived. According to
the analysis of the Poincar\'e sections, we found the localized quasi-periodic
and chaotic trajectories in the three-level hierarchical model. Moreover,
studies of correlation functions shown that the power spectrum for three-level
model possesses local maxima characterizing temporal scales with strong
correlation. Using the Fourier analysis of the solution's components, we have
studied the distribution of energy injected in the system over hierarchical
levels. Dynamical phenomena in the multi-level system were studied as well.</abstract><doi>10.48550/arxiv.1503.05759</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Physics - Chaotic Dynamics |
| title | Energy redistribution in hierarchical systems of oscillators |
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