Statistical properties of dynamical chaos
This study presents a survey of the results obtained by the authors on statistical description of dynamical chaos and the effect of noise ondynamical regimes. We deal with nearly hyperbolic and nonhyperbolic chaoticattractors and discuss methods of diagnosing the type of an attractor. Weconsider reg...
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| Format: | Article |
| Language: | English |
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AIMS Press
2004-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2004.1.161 |
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| author | Vadim S. Anishchenko Tatjana E. Vadivasova Galina I. Strelkova George A. Okrokvertskhov |
| author_facet | Vadim S. Anishchenko Tatjana E. Vadivasova Galina I. Strelkova George A. Okrokvertskhov |
| author_sort | Vadim S. Anishchenko |
| collection | DOAJ |
| description | This study presents a survey of the results obtained by the authors on statistical description of dynamical chaos and the effect of noise ondynamical regimes. We deal with nearly hyperbolic and nonhyperbolic chaoticattractors and discuss methods of diagnosing the type of an attractor. Weconsider regularities of the relaxation to an invariant probability measure fordifferent types of attractors. We explore peculiarities of autocorrelation decay and of power spectrum shape and their interconnection with Lyapunovexponents, instantaneous phase diffusion and the intensity of external noise.Numeric results are compared with experimental data. |
| format | Article |
| id | doaj-art-f61188ba202b4108a8b969d8fb20af57 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2004-02-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-f61188ba202b4108a8b969d8fb20af572025-01-24T01:46:28ZengAIMS PressMathematical Biosciences and Engineering1551-00182004-02-011116118410.3934/mbe.2004.1.161Statistical properties of dynamical chaosVadim S. Anishchenko0Tatjana E. Vadivasova1Galina I. Strelkova2George A. Okrokvertskhov3Institute of Nonlinear Dynamics, Department of Physics, Saratov State University, 83, Astrakhanskaya str., 410012, SaratovInstitute of Nonlinear Dynamics, Department of Physics, Saratov State University, 83, Astrakhanskaya str., 410012, SaratovInstitute of Nonlinear Dynamics, Department of Physics, Saratov State University, 83, Astrakhanskaya str., 410012, SaratovInstitute of Nonlinear Dynamics, Department of Physics, Saratov State University, 83, Astrakhanskaya str., 410012, SaratovThis study presents a survey of the results obtained by the authors on statistical description of dynamical chaos and the effect of noise ondynamical regimes. We deal with nearly hyperbolic and nonhyperbolic chaoticattractors and discuss methods of diagnosing the type of an attractor. Weconsider regularities of the relaxation to an invariant probability measure fordifferent types of attractors. We explore peculiarities of autocorrelation decay and of power spectrum shape and their interconnection with Lyapunovexponents, instantaneous phase diffusion and the intensity of external noise.Numeric results are compared with experimental data.https://www.aimspress.com/article/doi/10.3934/mbe.2004.1.161effective diffusion coefficient.phase variancenonhyperbolic attractorsspiral and funnel chaosautocorrelation functioninstantaneous phase |
| spellingShingle | Vadim S. Anishchenko Tatjana E. Vadivasova Galina I. Strelkova George A. Okrokvertskhov Statistical properties of dynamical chaos Mathematical Biosciences and Engineering effective diffusion coefficient. phase variance nonhyperbolic attractors spiral and funnel chaos autocorrelation function instantaneous phase |
| title | Statistical properties of dynamical chaos |
| title_full | Statistical properties of dynamical chaos |
| title_fullStr | Statistical properties of dynamical chaos |
| title_full_unstemmed | Statistical properties of dynamical chaos |
| title_short | Statistical properties of dynamical chaos |
| title_sort | statistical properties of dynamical chaos |
| topic | effective diffusion coefficient. phase variance nonhyperbolic attractors spiral and funnel chaos autocorrelation function instantaneous phase |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2004.1.161 |
| work_keys_str_mv | AT vadimsanishchenko statisticalpropertiesofdynamicalchaos AT tatjanaevadivasova statisticalpropertiesofdynamicalchaos AT galinaistrelkova statisticalpropertiesofdynamicalchaos AT georgeaokrokvertskhov statisticalpropertiesofdynamicalchaos |