Multistability of complex-valued neural networks with distributed delays
Abstract This paper addresses the multistability problem for the complex-valued neural networks with appropriate real–imaginary-type activation functions and distributed delays. Based on the geometrical properties of the activation functions and the fixed point theory, several sufficient criteria ar...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Gong, Weiqiang [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2016 |
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| Schlagwörter: |
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| Anmerkung: |
© The Natural Computing Applications Forum 2016 |
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| Übergeordnetes Werk: |
Enthalten in: Neural computing & applications - Springer London, 1993, 28(2016), Suppl 1 vom: 18. Apr., Seite 1-14 |
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| Übergeordnetes Werk: |
volume:28 ; year:2016 ; number:Suppl 1 ; day:18 ; month:04 ; pages:1-14 |
| Links: |
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| DOI / URN: |
10.1007/s00521-016-2305-9 |
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OLC2025600348 |
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| 520 | |a Abstract This paper addresses the multistability problem for the complex-valued neural networks with appropriate real–imaginary-type activation functions and distributed delays. Based on the geometrical properties of the activation functions and the fixed point theory, several sufficient criteria are obtained which not only guarantee the existence of $$9^n$$ equilibrium points but also assure the local exponential stability for the $$4^n$$ equilibrium points of them. Furthermore, the attraction basins of the $$4^n$$ equilibrium points are also estimated, which infers that the attraction basins could be enlarged under some mild restrictions. Finally, one numerical example is provided to illustrate the effectiveness of the obtained results. | ||
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| 700 | 1 | |a Zhang, Congjun |4 aut | |
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10.1007/s00521-016-2305-9 doi (DE-627)OLC2025600348 (DE-He213)s00521-016-2305-9-p DE-627 ger DE-627 rakwb eng 004 VZ Gong, Weiqiang verfasserin aut Multistability of complex-valued neural networks with distributed delays 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Natural Computing Applications Forum 2016 Abstract This paper addresses the multistability problem for the complex-valued neural networks with appropriate real–imaginary-type activation functions and distributed delays. Based on the geometrical properties of the activation functions and the fixed point theory, several sufficient criteria are obtained which not only guarantee the existence of $$9^n$$ equilibrium points but also assure the local exponential stability for the $$4^n$$ equilibrium points of them. Furthermore, the attraction basins of the $$4^n$$ equilibrium points are also estimated, which infers that the attraction basins could be enlarged under some mild restrictions. Finally, one numerical example is provided to illustrate the effectiveness of the obtained results. Complex-valued neural networks Multistability Distributed delays Attraction basin Liang, Jinling aut Zhang, Congjun aut Enthalten in Neural computing & applications Springer London, 1993 28(2016), Suppl 1 vom: 18. Apr., Seite 1-14 (DE-627)165669608 (DE-600)1136944-9 (DE-576)032873050 0941-0643 nnns volume:28 year:2016 number:Suppl 1 day:18 month:04 pages:1-14 https://doi.org/10.1007/s00521-016-2305-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_2018 GBV_ILN_4046 GBV_ILN_4277 AR 28 2016 Suppl 1 18 04 1-14 |
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10.1007/s00521-016-2305-9 doi (DE-627)OLC2025600348 (DE-He213)s00521-016-2305-9-p DE-627 ger DE-627 rakwb eng 004 VZ Gong, Weiqiang verfasserin aut Multistability of complex-valued neural networks with distributed delays 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Natural Computing Applications Forum 2016 Abstract This paper addresses the multistability problem for the complex-valued neural networks with appropriate real–imaginary-type activation functions and distributed delays. Based on the geometrical properties of the activation functions and the fixed point theory, several sufficient criteria are obtained which not only guarantee the existence of $$9^n$$ equilibrium points but also assure the local exponential stability for the $$4^n$$ equilibrium points of them. Furthermore, the attraction basins of the $$4^n$$ equilibrium points are also estimated, which infers that the attraction basins could be enlarged under some mild restrictions. Finally, one numerical example is provided to illustrate the effectiveness of the obtained results. Complex-valued neural networks Multistability Distributed delays Attraction basin Liang, Jinling aut Zhang, Congjun aut Enthalten in Neural computing & applications Springer London, 1993 28(2016), Suppl 1 vom: 18. Apr., Seite 1-14 (DE-627)165669608 (DE-600)1136944-9 (DE-576)032873050 0941-0643 nnns volume:28 year:2016 number:Suppl 1 day:18 month:04 pages:1-14 https://doi.org/10.1007/s00521-016-2305-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_2018 GBV_ILN_4046 GBV_ILN_4277 AR 28 2016 Suppl 1 18 04 1-14 |
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10.1007/s00521-016-2305-9 doi (DE-627)OLC2025600348 (DE-He213)s00521-016-2305-9-p DE-627 ger DE-627 rakwb eng 004 VZ Gong, Weiqiang verfasserin aut Multistability of complex-valued neural networks with distributed delays 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Natural Computing Applications Forum 2016 Abstract This paper addresses the multistability problem for the complex-valued neural networks with appropriate real–imaginary-type activation functions and distributed delays. Based on the geometrical properties of the activation functions and the fixed point theory, several sufficient criteria are obtained which not only guarantee the existence of $$9^n$$ equilibrium points but also assure the local exponential stability for the $$4^n$$ equilibrium points of them. Furthermore, the attraction basins of the $$4^n$$ equilibrium points are also estimated, which infers that the attraction basins could be enlarged under some mild restrictions. Finally, one numerical example is provided to illustrate the effectiveness of the obtained results. Complex-valued neural networks Multistability Distributed delays Attraction basin Liang, Jinling aut Zhang, Congjun aut Enthalten in Neural computing & applications Springer London, 1993 28(2016), Suppl 1 vom: 18. Apr., Seite 1-14 (DE-627)165669608 (DE-600)1136944-9 (DE-576)032873050 0941-0643 nnns volume:28 year:2016 number:Suppl 1 day:18 month:04 pages:1-14 https://doi.org/10.1007/s00521-016-2305-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_2018 GBV_ILN_4046 GBV_ILN_4277 AR 28 2016 Suppl 1 18 04 1-14 |
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10.1007/s00521-016-2305-9 doi (DE-627)OLC2025600348 (DE-He213)s00521-016-2305-9-p DE-627 ger DE-627 rakwb eng 004 VZ Gong, Weiqiang verfasserin aut Multistability of complex-valued neural networks with distributed delays 2016 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © The Natural Computing Applications Forum 2016 Abstract This paper addresses the multistability problem for the complex-valued neural networks with appropriate real–imaginary-type activation functions and distributed delays. Based on the geometrical properties of the activation functions and the fixed point theory, several sufficient criteria are obtained which not only guarantee the existence of $$9^n$$ equilibrium points but also assure the local exponential stability for the $$4^n$$ equilibrium points of them. Furthermore, the attraction basins of the $$4^n$$ equilibrium points are also estimated, which infers that the attraction basins could be enlarged under some mild restrictions. Finally, one numerical example is provided to illustrate the effectiveness of the obtained results. Complex-valued neural networks Multistability Distributed delays Attraction basin Liang, Jinling aut Zhang, Congjun aut Enthalten in Neural computing & applications Springer London, 1993 28(2016), Suppl 1 vom: 18. Apr., Seite 1-14 (DE-627)165669608 (DE-600)1136944-9 (DE-576)032873050 0941-0643 nnns volume:28 year:2016 number:Suppl 1 day:18 month:04 pages:1-14 https://doi.org/10.1007/s00521-016-2305-9 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT GBV_ILN_70 GBV_ILN_2018 GBV_ILN_4046 GBV_ILN_4277 AR 28 2016 Suppl 1 18 04 1-14 |
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Abstract This paper addresses the multistability problem for the complex-valued neural networks with appropriate real–imaginary-type activation functions and distributed delays. Based on the geometrical properties of the activation functions and the fixed point theory, several sufficient criteria are obtained which not only guarantee the existence of $$9^n$$ equilibrium points but also assure the local exponential stability for the $$4^n$$ equilibrium points of them. Furthermore, the attraction basins of the $$4^n$$ equilibrium points are also estimated, which infers that the attraction basins could be enlarged under some mild restrictions. Finally, one numerical example is provided to illustrate the effectiveness of the obtained results. © The Natural Computing Applications Forum 2016 |
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Abstract This paper addresses the multistability problem for the complex-valued neural networks with appropriate real–imaginary-type activation functions and distributed delays. Based on the geometrical properties of the activation functions and the fixed point theory, several sufficient criteria are obtained which not only guarantee the existence of $$9^n$$ equilibrium points but also assure the local exponential stability for the $$4^n$$ equilibrium points of them. Furthermore, the attraction basins of the $$4^n$$ equilibrium points are also estimated, which infers that the attraction basins could be enlarged under some mild restrictions. Finally, one numerical example is provided to illustrate the effectiveness of the obtained results. © The Natural Computing Applications Forum 2016 |
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Abstract This paper addresses the multistability problem for the complex-valued neural networks with appropriate real–imaginary-type activation functions and distributed delays. Based on the geometrical properties of the activation functions and the fixed point theory, several sufficient criteria are obtained which not only guarantee the existence of $$9^n$$ equilibrium points but also assure the local exponential stability for the $$4^n$$ equilibrium points of them. Furthermore, the attraction basins of the $$4^n$$ equilibrium points are also estimated, which infers that the attraction basins could be enlarged under some mild restrictions. Finally, one numerical example is provided to illustrate the effectiveness of the obtained results. © The Natural Computing Applications Forum 2016 |
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<?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01000caa a22002652 4500</leader><controlfield tag="001">OLC2025600348</controlfield><controlfield tag="003">DE-627</controlfield><controlfield tag="005">20230502114708.0</controlfield><controlfield tag="007">tu</controlfield><controlfield tag="008">200820s2016 xx ||||| 00| ||eng c</controlfield><datafield tag="024" ind1="7" ind2=" "><subfield code="a">10.1007/s00521-016-2305-9</subfield><subfield code="2">doi</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-627)OLC2025600348</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-He213)s00521-016-2305-9-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">004</subfield><subfield code="q">VZ</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Gong, Weiqiang</subfield><subfield code="e">verfasserin</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Multistability of complex-valued neural networks with distributed delays</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="c">2016</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">© The Natural Computing Applications Forum 2016</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract This paper addresses the multistability problem for the complex-valued neural networks with appropriate real–imaginary-type activation functions and distributed delays. 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Finally, one numerical example is provided to illustrate the effectiveness of the obtained results.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Complex-valued neural networks</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Multistability</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Distributed delays</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Attraction basin</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Liang, Jinling</subfield><subfield code="4">aut</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Zhang, Congjun</subfield><subfield code="4">aut</subfield></datafield><datafield tag="773" ind1="0" ind2="8"><subfield code="i">Enthalten in</subfield><subfield code="t">Neural computing & applications</subfield><subfield code="d">Springer London, 1993</subfield><subfield code="g">28(2016), Suppl 1 vom: 18. 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