Period-doubling bifurcation in an extended van der Pol system with bounded random parameter
An extended van der Pol system with bounded random parameter subjected to harmonic excitation is investigated by Chebyshev polynomial approximation. Firstly the stochastic extended van der Pol system is reduced into its equivalent deterministic one, solvable by suitable numerical methods. Then we ex...
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| Veröffentlicht in: | Communications in nonlinear science & numerical simulation 2008-12, Vol.13 (10), p.2256-2265 |
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| creator | Ma, Shaojuan Xu, Wei |
| description | An extended van der Pol system with bounded random parameter subjected to harmonic excitation is investigated by Chebyshev polynomial approximation. Firstly the stochastic extended van der Pol system is reduced into its equivalent deterministic one, solvable by suitable numerical methods. Then we explored nonlinear dynamical behavior about period-doubling bifurcation in stochastic system. Numerical simulations show that similar to the conventional period-doubling phenomenon in deterministic extended van der Pol system, stochastic period-doubling bifurcation may also occur in the stochastic extended van der Pol system. Besides, different from the deterministic case, in addition to the conventional bifurcation parameters, i.e. the amplitude and frequency of harmonic excitation, in the stochastic case the intensity of random parameter should also be taken as a new bifurcation parameter. |
| doi_str_mv | 10.1016/j.cnsns.2007.05.030 |
| format | Article |
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Firstly the stochastic extended van der Pol system is reduced into its equivalent deterministic one, solvable by suitable numerical methods. Then we explored nonlinear dynamical behavior about period-doubling bifurcation in stochastic system. Numerical simulations show that similar to the conventional period-doubling phenomenon in deterministic extended van der Pol system, stochastic period-doubling bifurcation may also occur in the stochastic extended van der Pol system. Besides, different from the deterministic case, in addition to the conventional bifurcation parameters, i.e. the amplitude and frequency of harmonic excitation, in the stochastic case the intensity of random parameter should also be taken as a new bifurcation parameter.</description><identifier>ISSN: 1007-5704</identifier><identifier>EISSN: 1878-7274</identifier><identifier>DOI: 10.1016/j.cnsns.2007.05.030</identifier><language>eng</language><publisher>Elsevier B.V</publisher><subject>Arch-like probability density function ; Chebyshev polynomial approximation ; Extended van der Pol system ; Period-doubling bifurcation</subject><ispartof>Communications in nonlinear science & numerical simulation, 2008-12, Vol.13 (10), p.2256-2265</ispartof><rights>2007 Elsevier B.V.</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c334t-ee9ef4639b220b86e636f460b191f2d7c8301e8dc498323f7a26b691973580973</citedby><cites>FETCH-LOGICAL-c334t-ee9ef4639b220b86e636f460b191f2d7c8301e8dc498323f7a26b691973580973</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://www.sciencedirect.com/science/article/pii/S100757040700158X$$EHTML$$P50$$Gelsevier$$H</linktohtml><link.rule.ids>314,776,780,3536,27903,27904,65309</link.rule.ids></links><search><creatorcontrib>Ma, Shaojuan</creatorcontrib><creatorcontrib>Xu, Wei</creatorcontrib><title>Period-doubling bifurcation in an extended van der Pol system with bounded random parameter</title><title>Communications in nonlinear science & numerical simulation</title><description>An extended van der Pol system with bounded random parameter subjected to harmonic excitation is investigated by Chebyshev polynomial approximation. Firstly the stochastic extended van der Pol system is reduced into its equivalent deterministic one, solvable by suitable numerical methods. Then we explored nonlinear dynamical behavior about period-doubling bifurcation in stochastic system. Numerical simulations show that similar to the conventional period-doubling phenomenon in deterministic extended van der Pol system, stochastic period-doubling bifurcation may also occur in the stochastic extended van der Pol system. Besides, different from the deterministic case, in addition to the conventional bifurcation parameters, i.e. the amplitude and frequency of harmonic excitation, in the stochastic case the intensity of random parameter should also be taken as a new bifurcation parameter.</description><subject>Arch-like probability density function</subject><subject>Chebyshev polynomial approximation</subject><subject>Extended van der Pol system</subject><subject>Period-doubling bifurcation</subject><issn>1007-5704</issn><issn>1878-7274</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2008</creationdate><recordtype>article</recordtype><recordid>eNp9ULtOAzEQtBBIhMAX0Liiu8OPe_gKChTxkiKRAioKy2fvgaM7O9h3QP4eJ6Gm2d3RzOxqB6FLSnJKaHW9zrWLLuaMkDonZU44OUIzKmqR1awujtOcmKysSXGKzmJck-RqymKG3lYQrDeZ8VPbW_eOW9tNQavReoetw8ph-BnBGTD4KwEDAa98j-M2jjDgbzt-4NZPez4oZ_yANyqoAUYI5-ikU32Ei78-R6_3dy-Lx2z5_PC0uF1mmvNizAAa6IqKNy1jpBUVVLxKmLS0oR0ztRacUBBGF43gjHe1YlVbNbSpeSlIqnN0ddi7Cf5zgjjKwUYNfa8c-CnKdIU3grEk5AehDj7GAJ3cBDuosJWUyF2Qci33QcpdkJKUMgWZXDcHF6QfviwEGbUFp8HYAHqUxtt__b_5fX1m</recordid><startdate>200812</startdate><enddate>200812</enddate><creator>Ma, Shaojuan</creator><creator>Xu, Wei</creator><general>Elsevier B.V</general><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>7TB</scope><scope>8FD</scope><scope>FR3</scope><scope>JQ2</scope><scope>KR7</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>200812</creationdate><title>Period-doubling bifurcation in an extended van der Pol system with bounded random parameter</title><author>Ma, Shaojuan ; Xu, Wei</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c334t-ee9ef4639b220b86e636f460b191f2d7c8301e8dc498323f7a26b691973580973</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2008</creationdate><topic>Arch-like probability density function</topic><topic>Chebyshev polynomial approximation</topic><topic>Extended van der Pol system</topic><topic>Period-doubling bifurcation</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ma, Shaojuan</creatorcontrib><creatorcontrib>Xu, Wei</creatorcontrib><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Mechanical & Transportation Engineering Abstracts</collection><collection>Technology Research Database</collection><collection>Engineering Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Civil Engineering Abstracts</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Communications in nonlinear science & numerical simulation</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ma, Shaojuan</au><au>Xu, Wei</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Period-doubling bifurcation in an extended van der Pol system with bounded random parameter</atitle><jtitle>Communications in nonlinear science & numerical simulation</jtitle><date>2008-12</date><risdate>2008</risdate><volume>13</volume><issue>10</issue><spage>2256</spage><epage>2265</epage><pages>2256-2265</pages><issn>1007-5704</issn><eissn>1878-7274</eissn><abstract>An extended van der Pol system with bounded random parameter subjected to harmonic excitation is investigated by Chebyshev polynomial approximation. Firstly the stochastic extended van der Pol system is reduced into its equivalent deterministic one, solvable by suitable numerical methods. Then we explored nonlinear dynamical behavior about period-doubling bifurcation in stochastic system. Numerical simulations show that similar to the conventional period-doubling phenomenon in deterministic extended van der Pol system, stochastic period-doubling bifurcation may also occur in the stochastic extended van der Pol system. Besides, different from the deterministic case, in addition to the conventional bifurcation parameters, i.e. the amplitude and frequency of harmonic excitation, in the stochastic case the intensity of random parameter should also be taken as a new bifurcation parameter.</abstract><pub>Elsevier B.V</pub><doi>10.1016/j.cnsns.2007.05.030</doi><tpages>10</tpages></addata></record> |
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| source | Elsevier ScienceDirect Journals |
| subjects | Arch-like probability density function Chebyshev polynomial approximation Extended van der Pol system Period-doubling bifurcation |
| title | Period-doubling bifurcation in an extended van der Pol system with bounded random parameter |
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