Calculation of Hamilton energy and control of dynamical systems with different types of attractors
Strange attractors can be observed in chaotic and hyperchaotic systems. Most of the dynamical systems hold a finite number of attractors, while some chaotic systems can be controlled to present an infinite number of attractors by generating infinite equilibria. Chaos can also be triggered in some dy...
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| Veröffentlicht in: | Chaos (Woodbury, N.Y.) N.Y.), 2017-05, Vol.27 (5), p.053108-053108 |
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| container_title | Chaos (Woodbury, N.Y.) |
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| creator | Ma, Jun Wu, Fuqiang Jin, Wuyin Zhou, Ping Hayat, Tasawar |
| description | Strange attractors can be observed in chaotic and hyperchaotic systems. Most of the dynamical systems hold a finite number of attractors, while some chaotic systems can be controlled to present an infinite number of attractors by generating infinite equilibria. Chaos can also be triggered in some dynamical systems that can present hidden attractors, and the attractors in these dynamical systems find no equilibria and the basin of attraction is not connected with any equilibrium (the equilibria position meets certain restriction function). In this paper, Hamilton energy is calculated on the chaotic systems with different types of attractors, and energy modulation is used to control the chaos in these systems. The potential mechanism could be that negative feedback in energy can suppress the phase space and oscillating behaviors, and thus, the chaotic, periodical oscillators can be controlled. It could be effective to control other chaotic, hyperchaotic and even periodical oscillating systems as well. |
| doi_str_mv | 10.1063/1.4983469 |
| format | Article |
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Most of the dynamical systems hold a finite number of attractors, while some chaotic systems can be controlled to present an infinite number of attractors by generating infinite equilibria. Chaos can also be triggered in some dynamical systems that can present hidden attractors, and the attractors in these dynamical systems find no equilibria and the basin of attraction is not connected with any equilibrium (the equilibria position meets certain restriction function). In this paper, Hamilton energy is calculated on the chaotic systems with different types of attractors, and energy modulation is used to control the chaos in these systems. The potential mechanism could be that negative feedback in energy can suppress the phase space and oscillating behaviors, and thus, the chaotic, periodical oscillators can be controlled. 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It could be effective to control other chaotic, hyperchaotic and even periodical oscillating systems as well.</description><subject>Attractors (mathematics)</subject><subject>Chaos theory</subject><subject>Control systems</subject><subject>Dynamical systems</subject><subject>Economic models</subject><subject>Equilibrium</subject><subject>Mathematical analysis</subject><subject>Negative feedback</subject><subject>Oscillators</subject><subject>Strange attractors</subject><subject>System effectiveness</subject><issn>1054-1500</issn><issn>1089-7682</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2017</creationdate><recordtype>article</recordtype><recordid>eNp90MtKxDAUBuAgiveFLyAFNypUc22bpQzeQHCj65CmJ1ppmzFJlb69GWdUUJAsciAffw4_QgcEnxFcsHNyxmXFeCHX0DbBlczLoqLri1nwnAiMt9BOCC8YY0KZ2ERbtBJlkeQ2qme6M2OnY-uGzNnsRvdtF9MMA_inKdNDkxk3RO-6xXMzDQkY3WVhChH6kL238TlrWmvBwxCzOM0hLKSO0WsTnQ97aMPqLsD-6t5Fj1eXD7Ob_O7--nZ2cZcbVrGY04pzUmEwUBsjMeWNFpTVgmBWpAOykVZyAZrXpS5MaXRhJQhtG1piY2q2i46XuXPvXkcIUfVtMNB1egA3BkUkFiWTlMhEj37RFzf6IW2nKKGcS1mQKqmTpTLeheDBqrlve-0nRbBaFK-IWhWf7OEqcax7aL7lV9MJnC5BMG38rPvbvDn_k6Tmjf0P__36A33Mmk0</recordid><startdate>201705</startdate><enddate>201705</enddate><creator>Ma, Jun</creator><creator>Wu, Fuqiang</creator><creator>Jin, Wuyin</creator><creator>Zhou, Ping</creator><creator>Hayat, Tasawar</creator><general>American Institute of Physics</general><scope>NPM</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><scope>7X8</scope><orcidid>https://orcid.org/0000-0002-6127-000X</orcidid><orcidid>https://orcid.org/000000026127000X</orcidid></search><sort><creationdate>201705</creationdate><title>Calculation of Hamilton energy and control of dynamical systems with different types of attractors</title><author>Ma, Jun ; Wu, Fuqiang ; Jin, Wuyin ; Zhou, Ping ; Hayat, Tasawar</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c383t-2844180ecebcc9024da523b51036363e9d9f945ea4b7a6c7ca6f9e5afd270ccb3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2017</creationdate><topic>Attractors (mathematics)</topic><topic>Chaos theory</topic><topic>Control systems</topic><topic>Dynamical systems</topic><topic>Economic models</topic><topic>Equilibrium</topic><topic>Mathematical analysis</topic><topic>Negative feedback</topic><topic>Oscillators</topic><topic>Strange attractors</topic><topic>System effectiveness</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Ma, Jun</creatorcontrib><creatorcontrib>Wu, Fuqiang</creatorcontrib><creatorcontrib>Jin, Wuyin</creatorcontrib><creatorcontrib>Zhou, Ping</creatorcontrib><creatorcontrib>Hayat, Tasawar</creatorcontrib><collection>PubMed</collection><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>MEDLINE - Academic</collection><jtitle>Chaos (Woodbury, N.Y.)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Ma, Jun</au><au>Wu, Fuqiang</au><au>Jin, Wuyin</au><au>Zhou, Ping</au><au>Hayat, Tasawar</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Calculation of Hamilton energy and control of dynamical systems with different types of attractors</atitle><jtitle>Chaos (Woodbury, N.Y.)</jtitle><addtitle>Chaos</addtitle><date>2017-05</date><risdate>2017</risdate><volume>27</volume><issue>5</issue><spage>053108</spage><epage>053108</epage><pages>053108-053108</pages><issn>1054-1500</issn><eissn>1089-7682</eissn><coden>CHAOEH</coden><abstract>Strange attractors can be observed in chaotic and hyperchaotic systems. Most of the dynamical systems hold a finite number of attractors, while some chaotic systems can be controlled to present an infinite number of attractors by generating infinite equilibria. Chaos can also be triggered in some dynamical systems that can present hidden attractors, and the attractors in these dynamical systems find no equilibria and the basin of attraction is not connected with any equilibrium (the equilibria position meets certain restriction function). In this paper, Hamilton energy is calculated on the chaotic systems with different types of attractors, and energy modulation is used to control the chaos in these systems. The potential mechanism could be that negative feedback in energy can suppress the phase space and oscillating behaviors, and thus, the chaotic, periodical oscillators can be controlled. 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| ispartof | Chaos (Woodbury, N.Y.), 2017-05, Vol.27 (5), p.053108-053108 |
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| language | eng |
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| source | AIP Journals Complete; Alma/SFX Local Collection |
| subjects | Attractors (mathematics) Chaos theory Control systems Dynamical systems Economic models Equilibrium Mathematical analysis Negative feedback Oscillators Strange attractors System effectiveness |
| title | Calculation of Hamilton energy and control of dynamical systems with different types of attractors |
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