Bifurcation characteristics analysis of a class of nonlinear dynamical systems based on singularity theory
A method for seeking main bifurcation parameters of a class of nonlinear dynamical systems is proposed. The method is based on the effects of parametric varia- tion of dynamical systems on eigenvalues of the Frechet matrix. The singularity theory is used to study the engineering unfolding （EU） and t...
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| Veröffentlicht in: | Applied mathematics and mechanics 2017-09, Vol.38 (9), p.1233-1246 |
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| container_title | Applied mathematics and mechanics |
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| creator | Lu, Kuan Chen, Yushu Hou, Lei |
| description | A method for seeking main bifurcation parameters of a class of nonlinear dynamical systems is proposed. The method is based on the effects of parametric varia- tion of dynamical systems on eigenvalues of the Frechet matrix. The singularity theory is used to study the engineering unfolding （EU） and the universal unfolding （UU） of an arch structure model, respectively. Unfolding parameters of EU are combination of concerned physical parameters in actual engineering, and equivalence of unfolding parameters and physical parameters is verified. Transient sets and bifurcation behaviors of EU and UU are compared to illustrate that EU can reflect main bifurcation characteristics of non- linear systems in engineering. The results improve the understanding and the scope of applicability of EU in actual engineering systems when UU is difficult to be obtained. |
| doi_str_mv | 10.1007/s10483-017-2234-8 |
| format | Article |
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The method is based on the effects of parametric varia- tion of dynamical systems on eigenvalues of the Frechet matrix. The singularity theory is used to study the engineering unfolding （EU） and the universal unfolding （UU） of an arch structure model, respectively. Unfolding parameters of EU are combination of concerned physical parameters in actual engineering, and equivalence of unfolding parameters and physical parameters is verified. Transient sets and bifurcation behaviors of EU and UU are compared to illustrate that EU can reflect main bifurcation characteristics of non- linear systems in engineering. 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The results improve the understanding and the scope of applicability of EU in actual engineering systems when UU is difficult to be obtained.</description><subject>Applications of Mathematics</subject><subject>Arches</subject><subject>Bifurcation theory</subject><subject>Classical Mechanics</subject><subject>Dynamical systems</subject><subject>Eigenvalues</subject><subject>Engineering</subject><subject>Fluid- and Aerodynamics</subject><subject>Mathematical Modeling and Industrial Mathematics</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Nonlinear dynamics</subject><subject>Partial Differential Equations</subject><subject>Physical properties</subject><issn>0253-4827</issn><issn>1573-2754</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp9kMtuFDEQRVsoSEwCH8DOgh1SQ_k1tpcQ8ZIisYG1VeO2ZzzqcSeuHpH-exw6Alasqhbn3lKdrnvJ4S0HMO-Ig7KyB256IaTq7ZNuw7WRvTBaXXQbEFr2ygrzrLskOgKAMkptuuOHnM414JynwsIBK4Y51kxzDsSw4LhQJjYlhiyMSL_XMpUxl4iVDUvBUw44MlpojidiO6Q4sNZFuezPI9Y8L2w-xKkuz7unCUeKLx7nVffj08fv11_6m2-fv16_v-mDNHbuDQIEdGCCdeAwOaF3PKVt2joXlYZktoM2ESPCAMYJLqxwg9q5pIyFHZdX3Zu19yeWhGXvj9O5tk_ILwvdH8Z7H0XzBK45aPDrFb6t09050vyX5k5IozUo3Si-UqFORDUmf1vzCeviOfgH_37171uvf_DvbcuINUONLftY_2n-T-jV46HDVPZ3Lffn0tZIcMKClb8AckSU2A</recordid><startdate>20170901</startdate><enddate>20170901</enddate><creator>Lu, Kuan</creator><creator>Chen, Yushu</creator><creator>Hou, Lei</creator><general>Shanghai University</general><general>Springer Nature B.V</general><general>School of Energy Science and Engineering, Harbin Institute of Technology,Harbin 150001, China</general><general>School of Astronautics, Harbin Institute of Technology, Harbin 150001, China</general><general>College of Engineering, The University of Iowa, Iowa City, IA 52242, U.S.A.%School of Astronautics, Harbin Institute of Technology, Harbin 150001, China%School of Astronautics, Harbin Institute of Technology, Harbin 150001, China</general><scope>2RA</scope><scope>92L</scope><scope>CQIGP</scope><scope>~WA</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>2B.</scope><scope>4A8</scope><scope>92I</scope><scope>93N</scope><scope>PSX</scope><scope>TCJ</scope></search><sort><creationdate>20170901</creationdate><title>Bifurcation characteristics analysis of a class of nonlinear dynamical systems based on singularity theory</title><author>Lu, Kuan ; Chen, Yushu ; Hou, Lei</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c378t-7a00ca907c8909af925b1ff6f699e450f76d57eaea0d079212829d4b9f4780b13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Applications of Mathematics</topic><topic>Arches</topic><topic>Bifurcation theory</topic><topic>Classical Mechanics</topic><topic>Dynamical systems</topic><topic>Eigenvalues</topic><topic>Engineering</topic><topic>Fluid- and Aerodynamics</topic><topic>Mathematical Modeling and Industrial Mathematics</topic><topic>Mathematics</topic><topic>Mathematics and Statistics</topic><topic>Nonlinear dynamics</topic><topic>Partial Differential Equations</topic><topic>Physical properties</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lu, Kuan</creatorcontrib><creatorcontrib>Chen, Yushu</creatorcontrib><creatorcontrib>Hou, Lei</creatorcontrib><collection>中文科技期刊数据库</collection><collection>中文科技期刊数据库-CALIS站点</collection><collection>中文科技期刊数据库-7.0平台</collection><collection>中文科技期刊数据库- 镜像站点</collection><collection>CrossRef</collection><collection>Wanfang Data Journals - Hong Kong</collection><collection>WANFANG Data Centre</collection><collection>Wanfang Data Journals</collection><collection>万方数据期刊 - 香港版</collection><collection>China Online Journals (COJ)</collection><collection>China Online Journals (COJ)</collection><jtitle>Applied mathematics and mechanics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lu, Kuan</au><au>Chen, Yushu</au><au>Hou, Lei</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Bifurcation characteristics analysis of a class of nonlinear dynamical systems based on singularity theory</atitle><jtitle>Applied mathematics and mechanics</jtitle><stitle>Appl. Math. Mech.-Engl. Ed</stitle><addtitle>Applied Mathematics and Mechanics（English Edition）</addtitle><date>2017-09-01</date><risdate>2017</risdate><volume>38</volume><issue>9</issue><spage>1233</spage><epage>1246</epage><pages>1233-1246</pages><issn>0253-4827</issn><eissn>1573-2754</eissn><abstract>A method for seeking main bifurcation parameters of a class of nonlinear dynamical systems is proposed. The method is based on the effects of parametric varia- tion of dynamical systems on eigenvalues of the Frechet matrix. The singularity theory is used to study the engineering unfolding （EU） and the universal unfolding （UU） of an arch structure model, respectively. Unfolding parameters of EU are combination of concerned physical parameters in actual engineering, and equivalence of unfolding parameters and physical parameters is verified. 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| ispartof | Applied mathematics and mechanics, 2017-09, Vol.38 (9), p.1233-1246 |
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| source | Alma/SFX Local Collection; SpringerLink Journals - AutoHoldings |
| subjects | Applications of Mathematics Arches Bifurcation theory Classical Mechanics Dynamical systems Eigenvalues Engineering Fluid- and Aerodynamics Mathematical Modeling and Industrial Mathematics Mathematics Mathematics and Statistics Nonlinear dynamics Partial Differential Equations Physical properties |
| title | Bifurcation characteristics analysis of a class of nonlinear dynamical systems based on singularity theory |
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