Dynamics of a Coupled Chua’s Circuit with Lossless Transmission Line
Abstract This paper proposes a coupled-circuit system composed of two Chua’s circuits with lossless transmission lines. By applying the Kirchhoff’s voltage and current laws, the equations that describe the coupled-circuit system are reduced to two coupled neutral-type differential equations with a t...
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| Autor*in: |
Dong, Tao [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2020 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media, LLC, part of Springer Nature 2020 |
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| Übergeordnetes Werk: |
Enthalten in: Circuits, systems and signal processing - Springer US, 1982, 40(2020), 4 vom: 29. Okt., Seite 1962-1985 |
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| Übergeordnetes Werk: |
volume:40 ; year:2020 ; number:4 ; day:29 ; month:10 ; pages:1962-1985 |
| Links: |
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| DOI / URN: |
10.1007/s00034-020-01563-y |
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OLC2124298216 |
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| 520 | |a Abstract This paper proposes a coupled-circuit system composed of two Chua’s circuits with lossless transmission lines. By applying the Kirchhoff’s voltage and current laws, the equations that describe the coupled-circuit system are reduced to two coupled neutral-type differential equations with a time delay. Subsequently, the conditions for global stability are established using the inequality technology, and those for local stability and Hopf bifurcation are obtained by selecting the length of the transmission line as the bifurcation parameter. By using the normal-form theory and central manifold theorem, the formulas for the Hopf bifurcation direction and bifurcation periodic solution are obtained. Finally, the numerical simulations not only verify the theoretical analysis but also show that chaos exists near the Hopf bifurcation point. | ||
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| 700 | 1 | |a Qiao, Xing |4 aut | |
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10.1007/s00034-020-01563-y doi (DE-627)OLC2124298216 (DE-He213)s00034-020-01563-y-p DE-627 ger DE-627 rakwb eng 600 VZ Dong, Tao verfasserin (orcid)0000-0003-0555-2720 aut Dynamics of a Coupled Chua’s Circuit with Lossless Transmission Line 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2020 Abstract This paper proposes a coupled-circuit system composed of two Chua’s circuits with lossless transmission lines. By applying the Kirchhoff’s voltage and current laws, the equations that describe the coupled-circuit system are reduced to two coupled neutral-type differential equations with a time delay. Subsequently, the conditions for global stability are established using the inequality technology, and those for local stability and Hopf bifurcation are obtained by selecting the length of the transmission line as the bifurcation parameter. By using the normal-form theory and central manifold theorem, the formulas for the Hopf bifurcation direction and bifurcation periodic solution are obtained. Finally, the numerical simulations not only verify the theoretical analysis but also show that chaos exists near the Hopf bifurcation point. Chua’s circuit Lossless transmission line Stability Hopf bifurcation Wang, Aiqing aut Qiao, Xing aut Enthalten in Circuits, systems and signal processing Springer US, 1982 40(2020), 4 vom: 29. Okt., Seite 1962-1985 (DE-627)130312134 (DE-600)588684-3 (DE-576)015889939 0278-081X nnns volume:40 year:2020 number:4 day:29 month:10 pages:1962-1985 https://doi.org/10.1007/s00034-020-01563-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC GBV_ILN_2244 AR 40 2020 4 29 10 1962-1985 |
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10.1007/s00034-020-01563-y doi (DE-627)OLC2124298216 (DE-He213)s00034-020-01563-y-p DE-627 ger DE-627 rakwb eng 600 VZ Dong, Tao verfasserin (orcid)0000-0003-0555-2720 aut Dynamics of a Coupled Chua’s Circuit with Lossless Transmission Line 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2020 Abstract This paper proposes a coupled-circuit system composed of two Chua’s circuits with lossless transmission lines. By applying the Kirchhoff’s voltage and current laws, the equations that describe the coupled-circuit system are reduced to two coupled neutral-type differential equations with a time delay. Subsequently, the conditions for global stability are established using the inequality technology, and those for local stability and Hopf bifurcation are obtained by selecting the length of the transmission line as the bifurcation parameter. By using the normal-form theory and central manifold theorem, the formulas for the Hopf bifurcation direction and bifurcation periodic solution are obtained. Finally, the numerical simulations not only verify the theoretical analysis but also show that chaos exists near the Hopf bifurcation point. Chua’s circuit Lossless transmission line Stability Hopf bifurcation Wang, Aiqing aut Qiao, Xing aut Enthalten in Circuits, systems and signal processing Springer US, 1982 40(2020), 4 vom: 29. Okt., Seite 1962-1985 (DE-627)130312134 (DE-600)588684-3 (DE-576)015889939 0278-081X nnns volume:40 year:2020 number:4 day:29 month:10 pages:1962-1985 https://doi.org/10.1007/s00034-020-01563-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC GBV_ILN_2244 AR 40 2020 4 29 10 1962-1985 |
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10.1007/s00034-020-01563-y doi (DE-627)OLC2124298216 (DE-He213)s00034-020-01563-y-p DE-627 ger DE-627 rakwb eng 600 VZ Dong, Tao verfasserin (orcid)0000-0003-0555-2720 aut Dynamics of a Coupled Chua’s Circuit with Lossless Transmission Line 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2020 Abstract This paper proposes a coupled-circuit system composed of two Chua’s circuits with lossless transmission lines. By applying the Kirchhoff’s voltage and current laws, the equations that describe the coupled-circuit system are reduced to two coupled neutral-type differential equations with a time delay. Subsequently, the conditions for global stability are established using the inequality technology, and those for local stability and Hopf bifurcation are obtained by selecting the length of the transmission line as the bifurcation parameter. By using the normal-form theory and central manifold theorem, the formulas for the Hopf bifurcation direction and bifurcation periodic solution are obtained. Finally, the numerical simulations not only verify the theoretical analysis but also show that chaos exists near the Hopf bifurcation point. Chua’s circuit Lossless transmission line Stability Hopf bifurcation Wang, Aiqing aut Qiao, Xing aut Enthalten in Circuits, systems and signal processing Springer US, 1982 40(2020), 4 vom: 29. Okt., Seite 1962-1985 (DE-627)130312134 (DE-600)588684-3 (DE-576)015889939 0278-081X nnns volume:40 year:2020 number:4 day:29 month:10 pages:1962-1985 https://doi.org/10.1007/s00034-020-01563-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC GBV_ILN_2244 AR 40 2020 4 29 10 1962-1985 |
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10.1007/s00034-020-01563-y doi (DE-627)OLC2124298216 (DE-He213)s00034-020-01563-y-p DE-627 ger DE-627 rakwb eng 600 VZ Dong, Tao verfasserin (orcid)0000-0003-0555-2720 aut Dynamics of a Coupled Chua’s Circuit with Lossless Transmission Line 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2020 Abstract This paper proposes a coupled-circuit system composed of two Chua’s circuits with lossless transmission lines. By applying the Kirchhoff’s voltage and current laws, the equations that describe the coupled-circuit system are reduced to two coupled neutral-type differential equations with a time delay. Subsequently, the conditions for global stability are established using the inequality technology, and those for local stability and Hopf bifurcation are obtained by selecting the length of the transmission line as the bifurcation parameter. By using the normal-form theory and central manifold theorem, the formulas for the Hopf bifurcation direction and bifurcation periodic solution are obtained. Finally, the numerical simulations not only verify the theoretical analysis but also show that chaos exists near the Hopf bifurcation point. Chua’s circuit Lossless transmission line Stability Hopf bifurcation Wang, Aiqing aut Qiao, Xing aut Enthalten in Circuits, systems and signal processing Springer US, 1982 40(2020), 4 vom: 29. Okt., Seite 1962-1985 (DE-627)130312134 (DE-600)588684-3 (DE-576)015889939 0278-081X nnns volume:40 year:2020 number:4 day:29 month:10 pages:1962-1985 https://doi.org/10.1007/s00034-020-01563-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC GBV_ILN_2244 AR 40 2020 4 29 10 1962-1985 |
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10.1007/s00034-020-01563-y doi (DE-627)OLC2124298216 (DE-He213)s00034-020-01563-y-p DE-627 ger DE-627 rakwb eng 600 VZ Dong, Tao verfasserin (orcid)0000-0003-0555-2720 aut Dynamics of a Coupled Chua’s Circuit with Lossless Transmission Line 2020 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media, LLC, part of Springer Nature 2020 Abstract This paper proposes a coupled-circuit system composed of two Chua’s circuits with lossless transmission lines. By applying the Kirchhoff’s voltage and current laws, the equations that describe the coupled-circuit system are reduced to two coupled neutral-type differential equations with a time delay. Subsequently, the conditions for global stability are established using the inequality technology, and those for local stability and Hopf bifurcation are obtained by selecting the length of the transmission line as the bifurcation parameter. By using the normal-form theory and central manifold theorem, the formulas for the Hopf bifurcation direction and bifurcation periodic solution are obtained. Finally, the numerical simulations not only verify the theoretical analysis but also show that chaos exists near the Hopf bifurcation point. Chua’s circuit Lossless transmission line Stability Hopf bifurcation Wang, Aiqing aut Qiao, Xing aut Enthalten in Circuits, systems and signal processing Springer US, 1982 40(2020), 4 vom: 29. Okt., Seite 1962-1985 (DE-627)130312134 (DE-600)588684-3 (DE-576)015889939 0278-081X nnns volume:40 year:2020 number:4 day:29 month:10 pages:1962-1985 https://doi.org/10.1007/s00034-020-01563-y lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-TEC GBV_ILN_2244 AR 40 2020 4 29 10 1962-1985 |
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Abstract This paper proposes a coupled-circuit system composed of two Chua’s circuits with lossless transmission lines. By applying the Kirchhoff’s voltage and current laws, the equations that describe the coupled-circuit system are reduced to two coupled neutral-type differential equations with a time delay. Subsequently, the conditions for global stability are established using the inequality technology, and those for local stability and Hopf bifurcation are obtained by selecting the length of the transmission line as the bifurcation parameter. By using the normal-form theory and central manifold theorem, the formulas for the Hopf bifurcation direction and bifurcation periodic solution are obtained. Finally, the numerical simulations not only verify the theoretical analysis but also show that chaos exists near the Hopf bifurcation point. © Springer Science+Business Media, LLC, part of Springer Nature 2020 |
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Abstract This paper proposes a coupled-circuit system composed of two Chua’s circuits with lossless transmission lines. By applying the Kirchhoff’s voltage and current laws, the equations that describe the coupled-circuit system are reduced to two coupled neutral-type differential equations with a time delay. Subsequently, the conditions for global stability are established using the inequality technology, and those for local stability and Hopf bifurcation are obtained by selecting the length of the transmission line as the bifurcation parameter. By using the normal-form theory and central manifold theorem, the formulas for the Hopf bifurcation direction and bifurcation periodic solution are obtained. Finally, the numerical simulations not only verify the theoretical analysis but also show that chaos exists near the Hopf bifurcation point. © Springer Science+Business Media, LLC, part of Springer Nature 2020 |
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Abstract This paper proposes a coupled-circuit system composed of two Chua’s circuits with lossless transmission lines. By applying the Kirchhoff’s voltage and current laws, the equations that describe the coupled-circuit system are reduced to two coupled neutral-type differential equations with a time delay. Subsequently, the conditions for global stability are established using the inequality technology, and those for local stability and Hopf bifurcation are obtained by selecting the length of the transmission line as the bifurcation parameter. By using the normal-form theory and central manifold theorem, the formulas for the Hopf bifurcation direction and bifurcation periodic solution are obtained. Finally, the numerical simulations not only verify the theoretical analysis but also show that chaos exists near the Hopf bifurcation point. © Springer Science+Business Media, LLC, part of Springer Nature 2020 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000naa a22002652 4500</leader><controlfield tag="001">OLC2124298216</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230505085134.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">230505s2020 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00034-020-01563-y</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2124298216</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s00034-020-01563-y-p</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-627</subfield><subfield code="b">ger</subfield><subfield code="c">DE-627</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1=" " ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="082" ind1="0" ind2="4"><subfield code="a">600</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Dong, Tao</subfield><subfield code="e">verfasserin</subfield><subfield code="0">(orcid)0000-0003-0555-2720</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Dynamics of a Coupled Chua’s Circuit with Lossless Transmission Line</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2020</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="a">Text</subfield><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="a">ohne Hilfsmittel zu benutzen</subfield><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="a">Band</subfield><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="500" ind1=" " ind2=" "><subfield code="a">© Springer Science+Business Media, LLC, part of Springer Nature 2020</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract This paper proposes a coupled-circuit system composed of two Chua’s circuits with lossless transmission lines. By applying the Kirchhoff’s voltage and current laws, the equations that describe the coupled-circuit system are reduced to two coupled neutral-type differential equations with a time delay. Subsequently, the conditions for global stability are established using the inequality technology, and those for local stability and Hopf bifurcation are obtained by selecting the length of the transmission line as the bifurcation parameter. By using the normal-form theory and central manifold theorem, the formulas for the Hopf bifurcation direction and bifurcation periodic solution are obtained. 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