Eintrag weiter verarbeiten
Generation and Evolution of Chaos in Double-Well Duffing Oscillator under Parametrical Excitation
Gespeichert in:
| Zeitschriftentitel: | Shock and Vibration |
|---|---|
| Personen und Körperschaften: | , , , , |
| In: | Shock and Vibration, 2016, 2016, S. 1-8 |
| Format: | E-Article |
| Sprache: | Englisch |
| veröffentlicht: |
Hindawi Limited
|
| Schlagwörter: |
| author_facet |
Zhang, Ying Yue, Xiaole Du, Lin Wang, Liang Fang, Tong Zhang, Ying Yue, Xiaole Du, Lin Wang, Liang Fang, Tong |
|---|---|
| author |
Zhang, Ying Yue, Xiaole Du, Lin Wang, Liang Fang, Tong |
| spellingShingle |
Zhang, Ying Yue, Xiaole Du, Lin Wang, Liang Fang, Tong Shock and Vibration Generation and Evolution of Chaos in Double-Well Duffing Oscillator under Parametrical Excitation Mechanical Engineering Mechanics of Materials Geotechnical Engineering and Engineering Geology Condensed Matter Physics Civil and Structural Engineering |
| author_sort |
zhang, ying |
| spelling |
Zhang, Ying Yue, Xiaole Du, Lin Wang, Liang Fang, Tong 1070-9622 1875-9203 Hindawi Limited Mechanical Engineering Mechanics of Materials Geotechnical Engineering and Engineering Geology Condensed Matter Physics Civil and Structural Engineering http://dx.doi.org/10.1155/2016/6109062 <jats:p>The generation and evolution of chaotic motion in double-well Duffing oscillator under harmonic parametrical excitation are investigated. Firstly, the complex dynamical behaviors are studied by applying multibifurcation diagram and Poincaré sections. Secondly, by means of Melnikov’s approach, the threshold value of parameter<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:math>for generation of chaotic behavior in Smale horseshoe sense is calculated. By the numerical simulation, it is obvious that as<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:math>exceeds this threshold value, the behavior of Duffing oscillator is still steady-state periodic but the transient motion is chaotic; until the top Lyapunov exponent turns to positive, the motion of system turns to permanent chaos. Therefore, in order to gain an insight into the evolution of chaotic behavior after<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:math>passing the threshold value, the transient motion, basin of attraction, and basin boundary are also investigated.</jats:p> Generation and Evolution of Chaos in Double-Well Duffing Oscillator under Parametrical Excitation Shock and Vibration |
| doi_str_mv |
10.1155/2016/6109062 |
| facet_avail |
Online Free |
| finc_class_facet |
Geographie Physik Technik Geologie und Paläontologie |
| format |
ElectronicArticle |
| fullrecord |
blob:ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMTE1NS8yMDE2LzYxMDkwNjI |
| id |
ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMTE1NS8yMDE2LzYxMDkwNjI |
| institution |
DE-Zi4 DE-Gla1 DE-15 DE-Pl11 DE-Rs1 DE-14 DE-105 DE-Ch1 DE-L229 DE-D275 DE-Bn3 DE-Brt1 DE-Zwi2 DE-D161 |
| imprint |
Hindawi Limited, 2016 |
| imprint_str_mv |
Hindawi Limited, 2016 |
| issn |
1070-9622 1875-9203 |
| issn_str_mv |
1070-9622 1875-9203 |
| language |
English |
| mega_collection |
Hindawi Limited (CrossRef) |
| match_str |
zhang2016generationandevolutionofchaosindoublewellduffingoscillatorunderparametricalexcitation |
| publishDateSort |
2016 |
| publisher |
Hindawi Limited |
| recordtype |
ai |
| record_format |
ai |
| series |
Shock and Vibration |
| source_id |
49 |
| title |
Generation and Evolution of Chaos in Double-Well Duffing Oscillator under Parametrical Excitation |
| title_unstemmed |
Generation and Evolution of Chaos in Double-Well Duffing Oscillator under Parametrical Excitation |
| title_full |
Generation and Evolution of Chaos in Double-Well Duffing Oscillator under Parametrical Excitation |
| title_fullStr |
Generation and Evolution of Chaos in Double-Well Duffing Oscillator under Parametrical Excitation |
| title_full_unstemmed |
Generation and Evolution of Chaos in Double-Well Duffing Oscillator under Parametrical Excitation |
| title_short |
Generation and Evolution of Chaos in Double-Well Duffing Oscillator under Parametrical Excitation |
| title_sort |
generation and evolution of chaos in double-well duffing oscillator under parametrical excitation |
| topic |
Mechanical Engineering Mechanics of Materials Geotechnical Engineering and Engineering Geology Condensed Matter Physics Civil and Structural Engineering |
| url |
http://dx.doi.org/10.1155/2016/6109062 |
| publishDate |
2016 |
| physical |
1-8 |
| description |
<jats:p>The generation and evolution of chaotic motion in double-well Duffing oscillator under harmonic parametrical excitation are investigated. Firstly, the complex dynamical behaviors are studied by applying multibifurcation diagram and Poincaré sections. Secondly, by means of Melnikov’s approach, the threshold value of parameter<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:math>for generation of chaotic behavior in Smale horseshoe sense is calculated. By the numerical simulation, it is obvious that as<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:math>exceeds this threshold value, the behavior of Duffing oscillator is still steady-state periodic but the transient motion is chaotic; until the top Lyapunov exponent turns to positive, the motion of system turns to permanent chaos. Therefore, in order to gain an insight into the evolution of chaotic behavior after<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:math>passing the threshold value, the transient motion, basin of attraction, and basin boundary are also investigated.</jats:p> |
| container_start_page |
1 |
| container_title |
Shock and Vibration |
| container_volume |
2016 |
| format_de105 |
Article, E-Article |
| format_de14 |
Article, E-Article |
| format_de15 |
Article, E-Article |
| format_de520 |
Article, E-Article |
| format_de540 |
Article, E-Article |
| format_dech1 |
Article, E-Article |
| format_ded117 |
Article, E-Article |
| format_degla1 |
E-Article |
| format_del152 |
Buch |
| format_del189 |
Article, E-Article |
| format_dezi4 |
Article |
| format_dezwi2 |
Article, E-Article |
| format_finc |
Article, E-Article |
| format_nrw |
Article, E-Article |
| _version_ |
1792331861569044491 |
| geogr_code |
not assigned |
| last_indexed |
2024-03-01T13:47:41.55Z |
| geogr_code_person |
not assigned |
| openURL |
url_ver=Z39.88-2004&ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fvufind.svn.sourceforge.net%3Agenerator&rft.title=Generation+and+Evolution+of+Chaos+in+Double-Well+Duffing+Oscillator+under+Parametrical+Excitation&rft.date=2016-01-01&genre=article&issn=1875-9203&volume=2016&spage=1&epage=8&pages=1-8&jtitle=Shock+and+Vibration&atitle=Generation+and+Evolution+of+Chaos+in+Double-Well+Duffing+Oscillator+under+Parametrical+Excitation&aulast=Fang&aufirst=Tong&rft_id=info%3Adoi%2F10.1155%2F2016%2F6109062&rft.language%5B0%5D=eng |
| SOLR | |
| _version_ | 1792331861569044491 |
| author | Zhang, Ying, Yue, Xiaole, Du, Lin, Wang, Liang, Fang, Tong |
| author_facet | Zhang, Ying, Yue, Xiaole, Du, Lin, Wang, Liang, Fang, Tong, Zhang, Ying, Yue, Xiaole, Du, Lin, Wang, Liang, Fang, Tong |
| author_sort | zhang, ying |
| container_start_page | 1 |
| container_title | Shock and Vibration |
| container_volume | 2016 |
| description | <jats:p>The generation and evolution of chaotic motion in double-well Duffing oscillator under harmonic parametrical excitation are investigated. Firstly, the complex dynamical behaviors are studied by applying multibifurcation diagram and Poincaré sections. Secondly, by means of Melnikov’s approach, the threshold value of parameter<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:math>for generation of chaotic behavior in Smale horseshoe sense is calculated. By the numerical simulation, it is obvious that as<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:math>exceeds this threshold value, the behavior of Duffing oscillator is still steady-state periodic but the transient motion is chaotic; until the top Lyapunov exponent turns to positive, the motion of system turns to permanent chaos. Therefore, in order to gain an insight into the evolution of chaotic behavior after<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:math>passing the threshold value, the transient motion, basin of attraction, and basin boundary are also investigated.</jats:p> |
| doi_str_mv | 10.1155/2016/6109062 |
| facet_avail | Online, Free |
| finc_class_facet | Geographie, Physik, Technik, Geologie und Paläontologie |
| format | ElectronicArticle |
| format_de105 | Article, E-Article |
| format_de14 | Article, E-Article |
| format_de15 | Article, E-Article |
| format_de520 | Article, E-Article |
| format_de540 | Article, E-Article |
| format_dech1 | Article, E-Article |
| format_ded117 | Article, E-Article |
| format_degla1 | E-Article |
| format_del152 | Buch |
| format_del189 | Article, E-Article |
| format_dezi4 | Article |
| format_dezwi2 | Article, E-Article |
| format_finc | Article, E-Article |
| format_nrw | Article, E-Article |
| geogr_code | not assigned |
| geogr_code_person | not assigned |
| id | ai-49-aHR0cDovL2R4LmRvaS5vcmcvMTAuMTE1NS8yMDE2LzYxMDkwNjI |
| imprint | Hindawi Limited, 2016 |
| imprint_str_mv | Hindawi Limited, 2016 |
| institution | DE-Zi4, DE-Gla1, DE-15, DE-Pl11, DE-Rs1, DE-14, DE-105, DE-Ch1, DE-L229, DE-D275, DE-Bn3, DE-Brt1, DE-Zwi2, DE-D161 |
| issn | 1070-9622, 1875-9203 |
| issn_str_mv | 1070-9622, 1875-9203 |
| language | English |
| last_indexed | 2024-03-01T13:47:41.55Z |
| match_str | zhang2016generationandevolutionofchaosindoublewellduffingoscillatorunderparametricalexcitation |
| mega_collection | Hindawi Limited (CrossRef) |
| physical | 1-8 |
| publishDate | 2016 |
| publishDateSort | 2016 |
| publisher | Hindawi Limited |
| record_format | ai |
| recordtype | ai |
| series | Shock and Vibration |
| source_id | 49 |
| spelling | Zhang, Ying Yue, Xiaole Du, Lin Wang, Liang Fang, Tong 1070-9622 1875-9203 Hindawi Limited Mechanical Engineering Mechanics of Materials Geotechnical Engineering and Engineering Geology Condensed Matter Physics Civil and Structural Engineering http://dx.doi.org/10.1155/2016/6109062 <jats:p>The generation and evolution of chaotic motion in double-well Duffing oscillator under harmonic parametrical excitation are investigated. Firstly, the complex dynamical behaviors are studied by applying multibifurcation diagram and Poincaré sections. Secondly, by means of Melnikov’s approach, the threshold value of parameter<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:math>for generation of chaotic behavior in Smale horseshoe sense is calculated. By the numerical simulation, it is obvious that as<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:math>exceeds this threshold value, the behavior of Duffing oscillator is still steady-state periodic but the transient motion is chaotic; until the top Lyapunov exponent turns to positive, the motion of system turns to permanent chaos. Therefore, in order to gain an insight into the evolution of chaotic behavior after<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M3"><mml:mrow><mml:mi>μ</mml:mi></mml:mrow></mml:math>passing the threshold value, the transient motion, basin of attraction, and basin boundary are also investigated.</jats:p> Generation and Evolution of Chaos in Double-Well Duffing Oscillator under Parametrical Excitation Shock and Vibration |
| spellingShingle | Zhang, Ying, Yue, Xiaole, Du, Lin, Wang, Liang, Fang, Tong, Shock and Vibration, Generation and Evolution of Chaos in Double-Well Duffing Oscillator under Parametrical Excitation, Mechanical Engineering, Mechanics of Materials, Geotechnical Engineering and Engineering Geology, Condensed Matter Physics, Civil and Structural Engineering |
| title | Generation and Evolution of Chaos in Double-Well Duffing Oscillator under Parametrical Excitation |
| title_full | Generation and Evolution of Chaos in Double-Well Duffing Oscillator under Parametrical Excitation |
| title_fullStr | Generation and Evolution of Chaos in Double-Well Duffing Oscillator under Parametrical Excitation |
| title_full_unstemmed | Generation and Evolution of Chaos in Double-Well Duffing Oscillator under Parametrical Excitation |
| title_short | Generation and Evolution of Chaos in Double-Well Duffing Oscillator under Parametrical Excitation |
| title_sort | generation and evolution of chaos in double-well duffing oscillator under parametrical excitation |
| title_unstemmed | Generation and Evolution of Chaos in Double-Well Duffing Oscillator under Parametrical Excitation |
| topic | Mechanical Engineering, Mechanics of Materials, Geotechnical Engineering and Engineering Geology, Condensed Matter Physics, Civil and Structural Engineering |
| url | http://dx.doi.org/10.1155/2016/6109062 |