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Zero-Hopf bifurcation and Hopf bifurcation for smooth Chua’s system
Based on the fact that Chua’s system is a classic model system of electronic circuits, we first present modified Chua’s system with a smooth nonlinearity, described by a cubic polynomial in this paper. Then, we explore the distribution of the equilibrium points of the modified Chua circuit system. B...
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| Published in: | Advances in difference equations 2018-04, Vol.2018 (1), p.1-17, Article 141 |
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| cites | cdi_FETCH-LOGICAL-c425t-177ac4f36e0ff068e29813c269b5b781cb149838ca0df0de90492bedb8a8ec563 |
| container_end_page | 17 |
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| container_title | Advances in difference equations |
| container_volume | 2018 |
| creator | Li, Junze Liu, Yebei Wei, Zhouchao |
| description | Based on the fact that Chua’s system is a classic model system of electronic circuits, we first present modified Chua’s system with a smooth nonlinearity, described by a cubic polynomial in this paper. Then, we explore the distribution of the equilibrium points of the modified Chua circuit system. By using the averaging theory, we consider zero-Hopf bifurcation of the modified Chua system. Moreover, the existence of periodic solutions in the modified Chua system is derived from the classical Hopf bifurcation theorem. |
| doi_str_mv | 10.1186/s13662-018-1597-8 |
| format | article |
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Moreover, the existence of periodic solutions in the modified Chua system is derived from the classical Hopf bifurcation theorem.</description><identifier>ISSN: 1687-1847</identifier><identifier>ISSN: 1687-1839</identifier><identifier>EISSN: 1687-1847</identifier><identifier>DOI: 10.1186/s13662-018-1597-8</identifier><language>eng</language><publisher>Cham: Springer International Publishing</publisher><subject>Analysis ; Bifurcation theory ; Chua’s circuit system ; Circuits ; Classical Hopf bifurcation ; Difference and Functional Equations ; Economic models ; Electronic circuits ; Functional Analysis ; Hopf bifurcation ; Mathematics ; Mathematics and Statistics ; Ordinary Differential Equations ; Partial Differential Equations ; Periodic solution ; Thermal energy ; Zero-Hopf bifurcation</subject><ispartof>Advances in difference equations, 2018-04, Vol.2018 (1), p.1-17, Article 141</ispartof><rights>The Author(s) 2018</rights><rights>Advances in Difference Equations is a copyright of Springer, (2018). 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Moreover, the existence of periodic solutions in the modified Chua system is derived from the classical Hopf bifurcation theorem.</description><subject>Analysis</subject><subject>Bifurcation theory</subject><subject>Chua’s circuit system</subject><subject>Circuits</subject><subject>Classical Hopf bifurcation</subject><subject>Difference and Functional Equations</subject><subject>Economic models</subject><subject>Electronic circuits</subject><subject>Functional Analysis</subject><subject>Hopf bifurcation</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Ordinary Differential Equations</subject><subject>Partial Differential Equations</subject><subject>Periodic solution</subject><subject>Thermal energy</subject><subject>Zero-Hopf bifurcation</subject><issn>1687-1847</issn><issn>1687-1839</issn><issn>1687-1847</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid>PIMPY</sourceid><sourceid>DOA</sourceid><recordid>eNp1kM1KAzEQx4MoWKsP4G3BczSTbLLJUUq1hYIXvXgJ2WzSbmk3Ndk99OZr-Ho-iVtXVBBPMwz_j-GH0CWQawApbhIwISgmIDFwVWB5hEYgZIFB5sXxr_0UnaW0JoSqXMoRmj67GPAs7HxW1r6L1rR1aDLTVNmfow8xS9sQ2lU2WXXm_fUtZWmfWrc9RyfebJK7-Jpj9HQ3fZzM8OLhfj65XWCbU95iKApjc8-EI94TIR1VEpilQpW8LCTYEnIlmbSGVJ5UTpFc0dJVpTTSWS7YGM2H3CqYtd7FemviXgdT689DiEttYlvbjdNAKyCcMl7lPFeMStvzUdYSwihAyfqsqyFrF8NL51Kr16GLTf--poSBEAUnh0YYVDaGlKLz361A9IG8Hsjrnrw-kNey99DBk3pts3TxJ_l_0wcr_4Un</recordid><startdate>20180419</startdate><enddate>20180419</enddate><creator>Li, Junze</creator><creator>Liu, Yebei</creator><creator>Wei, Zhouchao</creator><general>Springer International Publishing</general><general>Springer Nature B.V</general><general>SpringerOpen</general><scope>C6C</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>3V.</scope><scope>7SC</scope><scope>7TB</scope><scope>7XB</scope><scope>8AL</scope><scope>8FD</scope><scope>8FE</scope><scope>8FG</scope><scope>8FK</scope><scope>ABJCF</scope><scope>ABUWG</scope><scope>AFKRA</scope><scope>ARAPS</scope><scope>AZQEC</scope><scope>BENPR</scope><scope>BGLVJ</scope><scope>CCPQU</scope><scope>DWQXO</scope><scope>FR3</scope><scope>GNUQQ</scope><scope>HCIFZ</scope><scope>JQ2</scope><scope>K7-</scope><scope>KR7</scope><scope>L6V</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope><scope>M0N</scope><scope>M7S</scope><scope>P5Z</scope><scope>P62</scope><scope>PIMPY</scope><scope>PQEST</scope><scope>PQQKQ</scope><scope>PQUKI</scope><scope>PRINS</scope><scope>PTHSS</scope><scope>Q9U</scope><scope>DOA</scope></search><sort><creationdate>20180419</creationdate><title>Zero-Hopf bifurcation and Hopf bifurcation for smooth Chua’s system</title><author>Li, Junze ; 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| ispartof | Advances in difference equations, 2018-04, Vol.2018 (1), p.1-17, Article 141 |
| issn | 1687-1847 1687-1839 1687-1847 |
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| subjects | Analysis Bifurcation theory Chua’s circuit system Circuits Classical Hopf bifurcation Difference and Functional Equations Economic models Electronic circuits Functional Analysis Hopf bifurcation Mathematics Mathematics and Statistics Ordinary Differential Equations Partial Differential Equations Periodic solution Thermal energy Zero-Hopf bifurcation |
| title | Zero-Hopf bifurcation and Hopf bifurcation for smooth Chua’s system |
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