Synchronization of Hypercomplex Neural Networks with Mixed Time-Varying Delays
Abstract This article discusses the fixed-time synchronization (FTS) of hypercomplex neural networks (HCNNs) with mixed time-varying delays. Unlike finite-time synchronization (FNTS) based on initial conditions, the settling time of FTS can be adjusted to meet the needs. The state vector, weight mat...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Baluni, Sapna [verfasserIn] K. Yadav, Vijay [verfasserIn] Das, Subir [verfasserIn] Cao, Jinde [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2024 |
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| Schlagwörter: |
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| Anmerkung: |
© The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Übergeordnetes Werk: |
Enthalten in: Cognitive Computation - Springer US, 2009, 16(2024), 3 vom: 11. März, Seite 888-908 |
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| Übergeordnetes Werk: |
volume:16 ; year:2024 ; number:3 ; day:11 ; month:03 ; pages:888-908 |
| Links: |
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| DOI / URN: |
10.1007/s12559-024-10253-9 |
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SPR056088485 |
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| 520 | |a Abstract This article discusses the fixed-time synchronization (FTS) of hypercomplex neural networks (HCNNs) with mixed time-varying delays. Unlike finite-time synchronization (FNTS) based on initial conditions, the settling time of FTS can be adjusted to meet the needs. The state vector, weight matrices, activation functions, and input vectors of HCNNs are all hypercomplex numbers. The techniques used in complex-valued neural networks (CVNNs) and quaternion-valued neural networks (QVNNs) cannot be used directly with HCNNs because they do not work with eight or more dimensions. To begin with, the decomposition method is used to split the HCNNs into $$(n+1)$$ real-valued neural networks (RVNNs) applying distributive law to handle non-commutativity and non-associativity. A nonlinear controller is constructed to synchronize the master-response systems of the HCNNs. Lyapunov-based method is used to prove the stability of an error system. The FTS of mixed time-varying delayed HCNNs is achieved using a suitable lemma, Lipschitz condition, appropriate Lyapunov functional construction, and designing suitable controllers. Two different algebraic criteria for settling time have been achieved by employing two distinct lemmas. It is demonstrated that the settling time derived from Lemma 1 produces a more precise result than that obtained from Lemma 2. Three numerical examples for CVNNs, QVNNs, and octonions-valued neural networks (OVNNs) are provided to demonstrate the efficacy and effectiveness of the proposed theoretical results. | ||
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10.1007/s12559-024-10253-9 doi (DE-627)SPR056088485 (SPR)s12559-024-10253-9-e DE-627 ger DE-627 rakwb eng 004 VZ Baluni, Sapna verfasserin aut Synchronization of Hypercomplex Neural Networks with Mixed Time-Varying Delays 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract This article discusses the fixed-time synchronization (FTS) of hypercomplex neural networks (HCNNs) with mixed time-varying delays. Unlike finite-time synchronization (FNTS) based on initial conditions, the settling time of FTS can be adjusted to meet the needs. The state vector, weight matrices, activation functions, and input vectors of HCNNs are all hypercomplex numbers. The techniques used in complex-valued neural networks (CVNNs) and quaternion-valued neural networks (QVNNs) cannot be used directly with HCNNs because they do not work with eight or more dimensions. To begin with, the decomposition method is used to split the HCNNs into $$(n+1)$$ real-valued neural networks (RVNNs) applying distributive law to handle non-commutativity and non-associativity. A nonlinear controller is constructed to synchronize the master-response systems of the HCNNs. Lyapunov-based method is used to prove the stability of an error system. The FTS of mixed time-varying delayed HCNNs is achieved using a suitable lemma, Lipschitz condition, appropriate Lyapunov functional construction, and designing suitable controllers. Two different algebraic criteria for settling time have been achieved by employing two distinct lemmas. It is demonstrated that the settling time derived from Lemma 1 produces a more precise result than that obtained from Lemma 2. Three numerical examples for CVNNs, QVNNs, and octonions-valued neural networks (OVNNs) are provided to demonstrate the efficacy and effectiveness of the proposed theoretical results. Hypercomplex neural network (dpeaa)DE-He213 Fixed-time synchronization (dpeaa)DE-He213 Finite-time synchronization (dpeaa)DE-He213 Lyapunov stability (dpeaa)DE-He213 Mixed time-varying delays (dpeaa)DE-He213 K. Yadav, Vijay verfasserin aut Das, Subir verfasserin aut Cao, Jinde verfasserin aut Enthalten in Cognitive Computation Springer US, 2009 16(2024), 3 vom: 11. März, Seite 888-908 (DE-627)594779472 (DE-600)2486574-6 1866-9964 nnns volume:16 year:2024 number:3 day:11 month:03 pages:888-908 https://dx.doi.org/10.1007/s12559-024-10253-9 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 16 2024 3 11 03 888-908 |
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10.1007/s12559-024-10253-9 doi (DE-627)SPR056088485 (SPR)s12559-024-10253-9-e DE-627 ger DE-627 rakwb eng 004 VZ Baluni, Sapna verfasserin aut Synchronization of Hypercomplex Neural Networks with Mixed Time-Varying Delays 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract This article discusses the fixed-time synchronization (FTS) of hypercomplex neural networks (HCNNs) with mixed time-varying delays. Unlike finite-time synchronization (FNTS) based on initial conditions, the settling time of FTS can be adjusted to meet the needs. The state vector, weight matrices, activation functions, and input vectors of HCNNs are all hypercomplex numbers. The techniques used in complex-valued neural networks (CVNNs) and quaternion-valued neural networks (QVNNs) cannot be used directly with HCNNs because they do not work with eight or more dimensions. To begin with, the decomposition method is used to split the HCNNs into $$(n+1)$$ real-valued neural networks (RVNNs) applying distributive law to handle non-commutativity and non-associativity. A nonlinear controller is constructed to synchronize the master-response systems of the HCNNs. Lyapunov-based method is used to prove the stability of an error system. The FTS of mixed time-varying delayed HCNNs is achieved using a suitable lemma, Lipschitz condition, appropriate Lyapunov functional construction, and designing suitable controllers. Two different algebraic criteria for settling time have been achieved by employing two distinct lemmas. It is demonstrated that the settling time derived from Lemma 1 produces a more precise result than that obtained from Lemma 2. Three numerical examples for CVNNs, QVNNs, and octonions-valued neural networks (OVNNs) are provided to demonstrate the efficacy and effectiveness of the proposed theoretical results. Hypercomplex neural network (dpeaa)DE-He213 Fixed-time synchronization (dpeaa)DE-He213 Finite-time synchronization (dpeaa)DE-He213 Lyapunov stability (dpeaa)DE-He213 Mixed time-varying delays (dpeaa)DE-He213 K. Yadav, Vijay verfasserin aut Das, Subir verfasserin aut Cao, Jinde verfasserin aut Enthalten in Cognitive Computation Springer US, 2009 16(2024), 3 vom: 11. März, Seite 888-908 (DE-627)594779472 (DE-600)2486574-6 1866-9964 nnns volume:16 year:2024 number:3 day:11 month:03 pages:888-908 https://dx.doi.org/10.1007/s12559-024-10253-9 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 16 2024 3 11 03 888-908 |
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10.1007/s12559-024-10253-9 doi (DE-627)SPR056088485 (SPR)s12559-024-10253-9-e DE-627 ger DE-627 rakwb eng 004 VZ Baluni, Sapna verfasserin aut Synchronization of Hypercomplex Neural Networks with Mixed Time-Varying Delays 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract This article discusses the fixed-time synchronization (FTS) of hypercomplex neural networks (HCNNs) with mixed time-varying delays. Unlike finite-time synchronization (FNTS) based on initial conditions, the settling time of FTS can be adjusted to meet the needs. The state vector, weight matrices, activation functions, and input vectors of HCNNs are all hypercomplex numbers. The techniques used in complex-valued neural networks (CVNNs) and quaternion-valued neural networks (QVNNs) cannot be used directly with HCNNs because they do not work with eight or more dimensions. To begin with, the decomposition method is used to split the HCNNs into $$(n+1)$$ real-valued neural networks (RVNNs) applying distributive law to handle non-commutativity and non-associativity. A nonlinear controller is constructed to synchronize the master-response systems of the HCNNs. Lyapunov-based method is used to prove the stability of an error system. The FTS of mixed time-varying delayed HCNNs is achieved using a suitable lemma, Lipschitz condition, appropriate Lyapunov functional construction, and designing suitable controllers. Two different algebraic criteria for settling time have been achieved by employing two distinct lemmas. It is demonstrated that the settling time derived from Lemma 1 produces a more precise result than that obtained from Lemma 2. Three numerical examples for CVNNs, QVNNs, and octonions-valued neural networks (OVNNs) are provided to demonstrate the efficacy and effectiveness of the proposed theoretical results. Hypercomplex neural network (dpeaa)DE-He213 Fixed-time synchronization (dpeaa)DE-He213 Finite-time synchronization (dpeaa)DE-He213 Lyapunov stability (dpeaa)DE-He213 Mixed time-varying delays (dpeaa)DE-He213 K. Yadav, Vijay verfasserin aut Das, Subir verfasserin aut Cao, Jinde verfasserin aut Enthalten in Cognitive Computation Springer US, 2009 16(2024), 3 vom: 11. März, Seite 888-908 (DE-627)594779472 (DE-600)2486574-6 1866-9964 nnns volume:16 year:2024 number:3 day:11 month:03 pages:888-908 https://dx.doi.org/10.1007/s12559-024-10253-9 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 16 2024 3 11 03 888-908 |
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10.1007/s12559-024-10253-9 doi (DE-627)SPR056088485 (SPR)s12559-024-10253-9-e DE-627 ger DE-627 rakwb eng 004 VZ Baluni, Sapna verfasserin aut Synchronization of Hypercomplex Neural Networks with Mixed Time-Varying Delays 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract This article discusses the fixed-time synchronization (FTS) of hypercomplex neural networks (HCNNs) with mixed time-varying delays. Unlike finite-time synchronization (FNTS) based on initial conditions, the settling time of FTS can be adjusted to meet the needs. The state vector, weight matrices, activation functions, and input vectors of HCNNs are all hypercomplex numbers. The techniques used in complex-valued neural networks (CVNNs) and quaternion-valued neural networks (QVNNs) cannot be used directly with HCNNs because they do not work with eight or more dimensions. To begin with, the decomposition method is used to split the HCNNs into $$(n+1)$$ real-valued neural networks (RVNNs) applying distributive law to handle non-commutativity and non-associativity. A nonlinear controller is constructed to synchronize the master-response systems of the HCNNs. Lyapunov-based method is used to prove the stability of an error system. The FTS of mixed time-varying delayed HCNNs is achieved using a suitable lemma, Lipschitz condition, appropriate Lyapunov functional construction, and designing suitable controllers. Two different algebraic criteria for settling time have been achieved by employing two distinct lemmas. It is demonstrated that the settling time derived from Lemma 1 produces a more precise result than that obtained from Lemma 2. Three numerical examples for CVNNs, QVNNs, and octonions-valued neural networks (OVNNs) are provided to demonstrate the efficacy and effectiveness of the proposed theoretical results. Hypercomplex neural network (dpeaa)DE-He213 Fixed-time synchronization (dpeaa)DE-He213 Finite-time synchronization (dpeaa)DE-He213 Lyapunov stability (dpeaa)DE-He213 Mixed time-varying delays (dpeaa)DE-He213 K. Yadav, Vijay verfasserin aut Das, Subir verfasserin aut Cao, Jinde verfasserin aut Enthalten in Cognitive Computation Springer US, 2009 16(2024), 3 vom: 11. März, Seite 888-908 (DE-627)594779472 (DE-600)2486574-6 1866-9964 nnns volume:16 year:2024 number:3 day:11 month:03 pages:888-908 https://dx.doi.org/10.1007/s12559-024-10253-9 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 16 2024 3 11 03 888-908 |
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10.1007/s12559-024-10253-9 doi (DE-627)SPR056088485 (SPR)s12559-024-10253-9-e DE-627 ger DE-627 rakwb eng 004 VZ Baluni, Sapna verfasserin aut Synchronization of Hypercomplex Neural Networks with Mixed Time-Varying Delays 2024 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. Abstract This article discusses the fixed-time synchronization (FTS) of hypercomplex neural networks (HCNNs) with mixed time-varying delays. Unlike finite-time synchronization (FNTS) based on initial conditions, the settling time of FTS can be adjusted to meet the needs. The state vector, weight matrices, activation functions, and input vectors of HCNNs are all hypercomplex numbers. The techniques used in complex-valued neural networks (CVNNs) and quaternion-valued neural networks (QVNNs) cannot be used directly with HCNNs because they do not work with eight or more dimensions. To begin with, the decomposition method is used to split the HCNNs into $$(n+1)$$ real-valued neural networks (RVNNs) applying distributive law to handle non-commutativity and non-associativity. A nonlinear controller is constructed to synchronize the master-response systems of the HCNNs. Lyapunov-based method is used to prove the stability of an error system. The FTS of mixed time-varying delayed HCNNs is achieved using a suitable lemma, Lipschitz condition, appropriate Lyapunov functional construction, and designing suitable controllers. Two different algebraic criteria for settling time have been achieved by employing two distinct lemmas. It is demonstrated that the settling time derived from Lemma 1 produces a more precise result than that obtained from Lemma 2. Three numerical examples for CVNNs, QVNNs, and octonions-valued neural networks (OVNNs) are provided to demonstrate the efficacy and effectiveness of the proposed theoretical results. Hypercomplex neural network (dpeaa)DE-He213 Fixed-time synchronization (dpeaa)DE-He213 Finite-time synchronization (dpeaa)DE-He213 Lyapunov stability (dpeaa)DE-He213 Mixed time-varying delays (dpeaa)DE-He213 K. Yadav, Vijay verfasserin aut Das, Subir verfasserin aut Cao, Jinde verfasserin aut Enthalten in Cognitive Computation Springer US, 2009 16(2024), 3 vom: 11. März, Seite 888-908 (DE-627)594779472 (DE-600)2486574-6 1866-9964 nnns volume:16 year:2024 number:3 day:11 month:03 pages:888-908 https://dx.doi.org/10.1007/s12559-024-10253-9 X:SPRINGER Resolving-System lizenzpflichtig Volltext SYSFLAG_0 GBV_SPRINGER GBV_ILN_11 GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4328 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 AR 16 2024 3 11 03 888-908 |
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.</subfield></datafield><datafield tag="520" ind1=" " ind2=" "><subfield code="a">Abstract This article discusses the fixed-time synchronization (FTS) of hypercomplex neural networks (HCNNs) with mixed time-varying delays. Unlike finite-time synchronization (FNTS) based on initial conditions, the settling time of FTS can be adjusted to meet the needs. The state vector, weight matrices, activation functions, and input vectors of HCNNs are all hypercomplex numbers. The techniques used in complex-valued neural networks (CVNNs) and quaternion-valued neural networks (QVNNs) cannot be used directly with HCNNs because they do not work with eight or more dimensions. To begin with, the decomposition method is used to split the HCNNs into $$(n+1)$$ real-valued neural networks (RVNNs) applying distributive law to handle non-commutativity and non-associativity. A nonlinear controller is constructed to synchronize the master-response systems of the HCNNs. Lyapunov-based method is used to prove the stability of an error system. The FTS of mixed time-varying delayed HCNNs is achieved using a suitable lemma, Lipschitz condition, appropriate Lyapunov functional construction, and designing suitable controllers. Two different algebraic criteria for settling time have been achieved by employing two distinct lemmas. It is demonstrated that the settling time derived from Lemma 1 produces a more precise result than that obtained from Lemma 2. Three numerical examples for CVNNs, QVNNs, and octonions-valued neural networks (OVNNs) are provided to demonstrate the efficacy and effectiveness of the proposed theoretical results.</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Hypercomplex neural network</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Fixed-time synchronization</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Finite-time synchronization</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Lyapunov stability</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mixed time-varying delays</subfield><subfield code="7">(dpeaa)DE-He213</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">K. 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Baluni, Sapna |
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synchronization of hypercomplex neural networks with mixed time-varying delays |
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Synchronization of Hypercomplex Neural Networks with Mixed Time-Varying Delays |
| abstract |
Abstract This article discusses the fixed-time synchronization (FTS) of hypercomplex neural networks (HCNNs) with mixed time-varying delays. Unlike finite-time synchronization (FNTS) based on initial conditions, the settling time of FTS can be adjusted to meet the needs. The state vector, weight matrices, activation functions, and input vectors of HCNNs are all hypercomplex numbers. The techniques used in complex-valued neural networks (CVNNs) and quaternion-valued neural networks (QVNNs) cannot be used directly with HCNNs because they do not work with eight or more dimensions. To begin with, the decomposition method is used to split the HCNNs into $$(n+1)$$ real-valued neural networks (RVNNs) applying distributive law to handle non-commutativity and non-associativity. A nonlinear controller is constructed to synchronize the master-response systems of the HCNNs. Lyapunov-based method is used to prove the stability of an error system. The FTS of mixed time-varying delayed HCNNs is achieved using a suitable lemma, Lipschitz condition, appropriate Lyapunov functional construction, and designing suitable controllers. Two different algebraic criteria for settling time have been achieved by employing two distinct lemmas. It is demonstrated that the settling time derived from Lemma 1 produces a more precise result than that obtained from Lemma 2. Three numerical examples for CVNNs, QVNNs, and octonions-valued neural networks (OVNNs) are provided to demonstrate the efficacy and effectiveness of the proposed theoretical results. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstractGer |
Abstract This article discusses the fixed-time synchronization (FTS) of hypercomplex neural networks (HCNNs) with mixed time-varying delays. Unlike finite-time synchronization (FNTS) based on initial conditions, the settling time of FTS can be adjusted to meet the needs. The state vector, weight matrices, activation functions, and input vectors of HCNNs are all hypercomplex numbers. The techniques used in complex-valued neural networks (CVNNs) and quaternion-valued neural networks (QVNNs) cannot be used directly with HCNNs because they do not work with eight or more dimensions. To begin with, the decomposition method is used to split the HCNNs into $$(n+1)$$ real-valued neural networks (RVNNs) applying distributive law to handle non-commutativity and non-associativity. A nonlinear controller is constructed to synchronize the master-response systems of the HCNNs. Lyapunov-based method is used to prove the stability of an error system. The FTS of mixed time-varying delayed HCNNs is achieved using a suitable lemma, Lipschitz condition, appropriate Lyapunov functional construction, and designing suitable controllers. Two different algebraic criteria for settling time have been achieved by employing two distinct lemmas. It is demonstrated that the settling time derived from Lemma 1 produces a more precise result than that obtained from Lemma 2. Three numerical examples for CVNNs, QVNNs, and octonions-valued neural networks (OVNNs) are provided to demonstrate the efficacy and effectiveness of the proposed theoretical results. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
| abstract_unstemmed |
Abstract This article discusses the fixed-time synchronization (FTS) of hypercomplex neural networks (HCNNs) with mixed time-varying delays. Unlike finite-time synchronization (FNTS) based on initial conditions, the settling time of FTS can be adjusted to meet the needs. The state vector, weight matrices, activation functions, and input vectors of HCNNs are all hypercomplex numbers. The techniques used in complex-valued neural networks (CVNNs) and quaternion-valued neural networks (QVNNs) cannot be used directly with HCNNs because they do not work with eight or more dimensions. To begin with, the decomposition method is used to split the HCNNs into $$(n+1)$$ real-valued neural networks (RVNNs) applying distributive law to handle non-commutativity and non-associativity. A nonlinear controller is constructed to synchronize the master-response systems of the HCNNs. Lyapunov-based method is used to prove the stability of an error system. The FTS of mixed time-varying delayed HCNNs is achieved using a suitable lemma, Lipschitz condition, appropriate Lyapunov functional construction, and designing suitable controllers. Two different algebraic criteria for settling time have been achieved by employing two distinct lemmas. It is demonstrated that the settling time derived from Lemma 1 produces a more precise result than that obtained from Lemma 2. Three numerical examples for CVNNs, QVNNs, and octonions-valued neural networks (OVNNs) are provided to demonstrate the efficacy and effectiveness of the proposed theoretical results. © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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Synchronization of Hypercomplex Neural Networks with Mixed Time-Varying Delays |
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https://dx.doi.org/10.1007/s12559-024-10253-9 |
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K. Yadav, Vijay Das, Subir Cao, Jinde |
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10.1007/s12559-024-10253-9 |
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2024-07-03T20:07:50.497Z |
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| score |
7.402231 |