A new way to compute the Lyapunov characteristic exponents for non-smooth and discontinues dynamical systems

Abstract One of the most important problems of nonlinear dynamics is related to the development of methods concerning the identification of the dynamical modes of the corresponding systems. The classical method is related to the calculation of the Lyapunov characteristic exponents (LCEs). Usually, t...
Ausführliche Beschreibung

Gespeichert in:

Autor*in:	Semenov, Mikhail E. [verfasserIn] Borzunov, Sergei V. Meleshenko, Peter A.

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	Lyapunov characteristic exponents Hysteresis Non-ideal relay Preisach operator Dahl model

Anmerkung:	© The Author(s), under exclusive licence to Springer Nature B.V. 2022

Übergeordnetes Werk:	Enthalten in: Nonlinear dynamics - Dordrecht [u.a.] : Springer Science + Business Media B.V, 1990, 109(2022), 3 vom: 09. Mai, Seite 1805-1821
Übergeordnetes Werk:	volume:109 ; year:2022 ; number:3 ; day:09 ; month:05 ; pages:1805-1821

Links:	Volltext

DOI / URN:	10.1007/s11071-022-07492-6

Katalog-ID:	SPR04779383X

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100	1		\|a Semenov, Mikhail E. \|e verfasserin \|0 (orcid)0000-0002-3361-1102 \|4 aut
245	1	2	\|a A new way to compute the Lyapunov characteristic exponents for non-smooth and discontinues dynamical systems
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520			\|a Abstract One of the most important problems of nonlinear dynamics is related to the development of methods concerning the identification of the dynamical modes of the corresponding systems. The classical method is related to the calculation of the Lyapunov characteristic exponents (LCEs). Usually, to implement the classical algorithms for the LCEs calculation, the smoothness of the right-hand sides of the corresponding equations is required. In this work, we propose a new algorithm for the LCEs computation in systems with strong nonlinearities (these nonlinearities cannot be linearized) including the hysteresis. This algorithm uses the values of the Jacobi matrix in the vicinity of singularities of the right-hand sides of the corresponding equations. The proposed modification of the algorithm is also can be used for systems containing such design hysteresis nonlinearity as the Preisach operator. (Thus, this modification can be used for all members of the hysteresis family.) Moreover, the proposed algorithm can be successfully applied to the well-known chaotic systems with smooth nonlinearities. Examples of dynamical systems with hysteresis nonlinearities, such as the Lorentz system with hysteresis friction and the van der Pol oscillator with hysteresis block, are considered. These examples illustrate the efficiency of the proposed algorithm.
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650		4	\|a Preisach operator \|7 (dpeaa)DE-He213
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700	1		\|a Borzunov, Sergei V. \|4 aut
700	1		\|a Meleshenko, Peter A. \|4 aut
773	0	8	\|i Enthalten in \|t Nonlinear dynamics \|d Dordrecht [u.a.] : Springer Science + Business Media B.V, 1990 \|g 109(2022), 3 vom: 09. Mai, Seite 1805-1821 \|w (DE-627)315297034 \|w (DE-600)2012600-1 \|x 1573-269X \|7 nnns
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912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
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912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
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912			\|a GBV_ILN_2093
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912			\|a GBV_ILN_2108
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allfields	10.1007/s11071-022-07492-6 doi (DE-627)SPR04779383X (SPR)s11071-022-07492-6-e DE-627 ger DE-627 rakwb eng Semenov, Mikhail E. verfasserin (orcid)0000-0002-3361-1102 aut A new way to compute the Lyapunov characteristic exponents for non-smooth and discontinues dynamical systems 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2022 Abstract One of the most important problems of nonlinear dynamics is related to the development of methods concerning the identification of the dynamical modes of the corresponding systems. The classical method is related to the calculation of the Lyapunov characteristic exponents (LCEs). Usually, to implement the classical algorithms for the LCEs calculation, the smoothness of the right-hand sides of the corresponding equations is required. In this work, we propose a new algorithm for the LCEs computation in systems with strong nonlinearities (these nonlinearities cannot be linearized) including the hysteresis. This algorithm uses the values of the Jacobi matrix in the vicinity of singularities of the right-hand sides of the corresponding equations. The proposed modification of the algorithm is also can be used for systems containing such design hysteresis nonlinearity as the Preisach operator. (Thus, this modification can be used for all members of the hysteresis family.) Moreover, the proposed algorithm can be successfully applied to the well-known chaotic systems with smooth nonlinearities. Examples of dynamical systems with hysteresis nonlinearities, such as the Lorentz system with hysteresis friction and the van der Pol oscillator with hysteresis block, are considered. These examples illustrate the efficiency of the proposed algorithm. Lyapunov characteristic exponents (dpeaa)DE-He213 Hysteresis (dpeaa)DE-He213 Non-ideal relay (dpeaa)DE-He213 Preisach operator (dpeaa)DE-He213 Dahl model (dpeaa)DE-He213 Borzunov, Sergei V. aut Meleshenko, Peter A. aut Enthalten in Nonlinear dynamics Dordrecht [u.a.] : Springer Science + Business Media B.V, 1990 109(2022), 3 vom: 09. Mai, Seite 1805-1821 (DE-627)315297034 (DE-600)2012600-1 1573-269X nnns volume:109 year:2022 number:3 day:09 month:05 pages:1805-1821 https://dx.doi.org/10.1007/s11071-022-07492-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 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_2008 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 109 2022 3 09 05 1805-1821
spelling	10.1007/s11071-022-07492-6 doi (DE-627)SPR04779383X (SPR)s11071-022-07492-6-e DE-627 ger DE-627 rakwb eng Semenov, Mikhail E. verfasserin (orcid)0000-0002-3361-1102 aut A new way to compute the Lyapunov characteristic exponents for non-smooth and discontinues dynamical systems 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2022 Abstract One of the most important problems of nonlinear dynamics is related to the development of methods concerning the identification of the dynamical modes of the corresponding systems. The classical method is related to the calculation of the Lyapunov characteristic exponents (LCEs). Usually, to implement the classical algorithms for the LCEs calculation, the smoothness of the right-hand sides of the corresponding equations is required. In this work, we propose a new algorithm for the LCEs computation in systems with strong nonlinearities (these nonlinearities cannot be linearized) including the hysteresis. This algorithm uses the values of the Jacobi matrix in the vicinity of singularities of the right-hand sides of the corresponding equations. The proposed modification of the algorithm is also can be used for systems containing such design hysteresis nonlinearity as the Preisach operator. (Thus, this modification can be used for all members of the hysteresis family.) Moreover, the proposed algorithm can be successfully applied to the well-known chaotic systems with smooth nonlinearities. Examples of dynamical systems with hysteresis nonlinearities, such as the Lorentz system with hysteresis friction and the van der Pol oscillator with hysteresis block, are considered. These examples illustrate the efficiency of the proposed algorithm. Lyapunov characteristic exponents (dpeaa)DE-He213 Hysteresis (dpeaa)DE-He213 Non-ideal relay (dpeaa)DE-He213 Preisach operator (dpeaa)DE-He213 Dahl model (dpeaa)DE-He213 Borzunov, Sergei V. aut Meleshenko, Peter A. aut Enthalten in Nonlinear dynamics Dordrecht [u.a.] : Springer Science + Business Media B.V, 1990 109(2022), 3 vom: 09. Mai, Seite 1805-1821 (DE-627)315297034 (DE-600)2012600-1 1573-269X nnns volume:109 year:2022 number:3 day:09 month:05 pages:1805-1821 https://dx.doi.org/10.1007/s11071-022-07492-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 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_2008 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 109 2022 3 09 05 1805-1821
allfields_unstemmed	10.1007/s11071-022-07492-6 doi (DE-627)SPR04779383X (SPR)s11071-022-07492-6-e DE-627 ger DE-627 rakwb eng Semenov, Mikhail E. verfasserin (orcid)0000-0002-3361-1102 aut A new way to compute the Lyapunov characteristic exponents for non-smooth and discontinues dynamical systems 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2022 Abstract One of the most important problems of nonlinear dynamics is related to the development of methods concerning the identification of the dynamical modes of the corresponding systems. The classical method is related to the calculation of the Lyapunov characteristic exponents (LCEs). Usually, to implement the classical algorithms for the LCEs calculation, the smoothness of the right-hand sides of the corresponding equations is required. In this work, we propose a new algorithm for the LCEs computation in systems with strong nonlinearities (these nonlinearities cannot be linearized) including the hysteresis. This algorithm uses the values of the Jacobi matrix in the vicinity of singularities of the right-hand sides of the corresponding equations. The proposed modification of the algorithm is also can be used for systems containing such design hysteresis nonlinearity as the Preisach operator. (Thus, this modification can be used for all members of the hysteresis family.) Moreover, the proposed algorithm can be successfully applied to the well-known chaotic systems with smooth nonlinearities. Examples of dynamical systems with hysteresis nonlinearities, such as the Lorentz system with hysteresis friction and the van der Pol oscillator with hysteresis block, are considered. These examples illustrate the efficiency of the proposed algorithm. Lyapunov characteristic exponents (dpeaa)DE-He213 Hysteresis (dpeaa)DE-He213 Non-ideal relay (dpeaa)DE-He213 Preisach operator (dpeaa)DE-He213 Dahl model (dpeaa)DE-He213 Borzunov, Sergei V. aut Meleshenko, Peter A. aut Enthalten in Nonlinear dynamics Dordrecht [u.a.] : Springer Science + Business Media B.V, 1990 109(2022), 3 vom: 09. Mai, Seite 1805-1821 (DE-627)315297034 (DE-600)2012600-1 1573-269X nnns volume:109 year:2022 number:3 day:09 month:05 pages:1805-1821 https://dx.doi.org/10.1007/s11071-022-07492-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 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_2008 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 109 2022 3 09 05 1805-1821
allfieldsGer	10.1007/s11071-022-07492-6 doi (DE-627)SPR04779383X (SPR)s11071-022-07492-6-e DE-627 ger DE-627 rakwb eng Semenov, Mikhail E. verfasserin (orcid)0000-0002-3361-1102 aut A new way to compute the Lyapunov characteristic exponents for non-smooth and discontinues dynamical systems 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2022 Abstract One of the most important problems of nonlinear dynamics is related to the development of methods concerning the identification of the dynamical modes of the corresponding systems. The classical method is related to the calculation of the Lyapunov characteristic exponents (LCEs). Usually, to implement the classical algorithms for the LCEs calculation, the smoothness of the right-hand sides of the corresponding equations is required. In this work, we propose a new algorithm for the LCEs computation in systems with strong nonlinearities (these nonlinearities cannot be linearized) including the hysteresis. This algorithm uses the values of the Jacobi matrix in the vicinity of singularities of the right-hand sides of the corresponding equations. The proposed modification of the algorithm is also can be used for systems containing such design hysteresis nonlinearity as the Preisach operator. (Thus, this modification can be used for all members of the hysteresis family.) Moreover, the proposed algorithm can be successfully applied to the well-known chaotic systems with smooth nonlinearities. Examples of dynamical systems with hysteresis nonlinearities, such as the Lorentz system with hysteresis friction and the van der Pol oscillator with hysteresis block, are considered. These examples illustrate the efficiency of the proposed algorithm. Lyapunov characteristic exponents (dpeaa)DE-He213 Hysteresis (dpeaa)DE-He213 Non-ideal relay (dpeaa)DE-He213 Preisach operator (dpeaa)DE-He213 Dahl model (dpeaa)DE-He213 Borzunov, Sergei V. aut Meleshenko, Peter A. aut Enthalten in Nonlinear dynamics Dordrecht [u.a.] : Springer Science + Business Media B.V, 1990 109(2022), 3 vom: 09. Mai, Seite 1805-1821 (DE-627)315297034 (DE-600)2012600-1 1573-269X nnns volume:109 year:2022 number:3 day:09 month:05 pages:1805-1821 https://dx.doi.org/10.1007/s11071-022-07492-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 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_2008 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 109 2022 3 09 05 1805-1821
allfieldsSound	10.1007/s11071-022-07492-6 doi (DE-627)SPR04779383X (SPR)s11071-022-07492-6-e DE-627 ger DE-627 rakwb eng Semenov, Mikhail E. verfasserin (orcid)0000-0002-3361-1102 aut A new way to compute the Lyapunov characteristic exponents for non-smooth and discontinues dynamical systems 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier © The Author(s), under exclusive licence to Springer Nature B.V. 2022 Abstract One of the most important problems of nonlinear dynamics is related to the development of methods concerning the identification of the dynamical modes of the corresponding systems. The classical method is related to the calculation of the Lyapunov characteristic exponents (LCEs). Usually, to implement the classical algorithms for the LCEs calculation, the smoothness of the right-hand sides of the corresponding equations is required. In this work, we propose a new algorithm for the LCEs computation in systems with strong nonlinearities (these nonlinearities cannot be linearized) including the hysteresis. This algorithm uses the values of the Jacobi matrix in the vicinity of singularities of the right-hand sides of the corresponding equations. The proposed modification of the algorithm is also can be used for systems containing such design hysteresis nonlinearity as the Preisach operator. (Thus, this modification can be used for all members of the hysteresis family.) Moreover, the proposed algorithm can be successfully applied to the well-known chaotic systems with smooth nonlinearities. Examples of dynamical systems with hysteresis nonlinearities, such as the Lorentz system with hysteresis friction and the van der Pol oscillator with hysteresis block, are considered. These examples illustrate the efficiency of the proposed algorithm. Lyapunov characteristic exponents (dpeaa)DE-He213 Hysteresis (dpeaa)DE-He213 Non-ideal relay (dpeaa)DE-He213 Preisach operator (dpeaa)DE-He213 Dahl model (dpeaa)DE-He213 Borzunov, Sergei V. aut Meleshenko, Peter A. aut Enthalten in Nonlinear dynamics Dordrecht [u.a.] : Springer Science + Business Media B.V, 1990 109(2022), 3 vom: 09. Mai, Seite 1805-1821 (DE-627)315297034 (DE-600)2012600-1 1573-269X nnns volume:109 year:2022 number:3 day:09 month:05 pages:1805-1821 https://dx.doi.org/10.1007/s11071-022-07492-6 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A 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_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 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_2008 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 109 2022 3 09 05 1805-1821
language	English
source	Enthalten in Nonlinear dynamics 109(2022), 3 vom: 09. Mai, Seite 1805-1821 volume:109 year:2022 number:3 day:09 month:05 pages:1805-1821
sourceStr	Enthalten in Nonlinear dynamics 109(2022), 3 vom: 09. Mai, Seite 1805-1821 volume:109 year:2022 number:3 day:09 month:05 pages:1805-1821
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institution	findex.gbv.de
topic_facet	Lyapunov characteristic exponents Hysteresis Non-ideal relay Preisach operator Dahl model
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container_title	Nonlinear dynamics
authorswithroles_txt_mv	Semenov, Mikhail E. @@aut@@ Borzunov, Sergei V. @@aut@@ Meleshenko, Peter A. @@aut@@
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author	Semenov, Mikhail E.
spellingShingle	Semenov, Mikhail E. misc Lyapunov characteristic exponents misc Hysteresis misc Non-ideal relay misc Preisach operator misc Dahl model A new way to compute the Lyapunov characteristic exponents for non-smooth and discontinues dynamical systems
authorStr	Semenov, Mikhail E.
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topic_title	A new way to compute the Lyapunov characteristic exponents for non-smooth and discontinues dynamical systems Lyapunov characteristic exponents (dpeaa)DE-He213 Hysteresis (dpeaa)DE-He213 Non-ideal relay (dpeaa)DE-He213 Preisach operator (dpeaa)DE-He213 Dahl model (dpeaa)DE-He213
topic	misc Lyapunov characteristic exponents misc Hysteresis misc Non-ideal relay misc Preisach operator misc Dahl model
topic_unstemmed	misc Lyapunov characteristic exponents misc Hysteresis misc Non-ideal relay misc Preisach operator misc Dahl model
topic_browse	misc Lyapunov characteristic exponents misc Hysteresis misc Non-ideal relay misc Preisach operator misc Dahl model
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title	A new way to compute the Lyapunov characteristic exponents for non-smooth and discontinues dynamical systems
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title_full	A new way to compute the Lyapunov characteristic exponents for non-smooth and discontinues dynamical systems
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author_browse	Semenov, Mikhail E. Borzunov, Sergei V. Meleshenko, Peter A.
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title_sort	new way to compute the lyapunov characteristic exponents for non-smooth and discontinues dynamical systems
title_auth	A new way to compute the Lyapunov characteristic exponents for non-smooth and discontinues dynamical systems
abstract	Abstract One of the most important problems of nonlinear dynamics is related to the development of methods concerning the identification of the dynamical modes of the corresponding systems. The classical method is related to the calculation of the Lyapunov characteristic exponents (LCEs). Usually, to implement the classical algorithms for the LCEs calculation, the smoothness of the right-hand sides of the corresponding equations is required. In this work, we propose a new algorithm for the LCEs computation in systems with strong nonlinearities (these nonlinearities cannot be linearized) including the hysteresis. This algorithm uses the values of the Jacobi matrix in the vicinity of singularities of the right-hand sides of the corresponding equations. The proposed modification of the algorithm is also can be used for systems containing such design hysteresis nonlinearity as the Preisach operator. (Thus, this modification can be used for all members of the hysteresis family.) Moreover, the proposed algorithm can be successfully applied to the well-known chaotic systems with smooth nonlinearities. Examples of dynamical systems with hysteresis nonlinearities, such as the Lorentz system with hysteresis friction and the van der Pol oscillator with hysteresis block, are considered. These examples illustrate the efficiency of the proposed algorithm. © The Author(s), under exclusive licence to Springer Nature B.V. 2022
abstractGer	Abstract One of the most important problems of nonlinear dynamics is related to the development of methods concerning the identification of the dynamical modes of the corresponding systems. The classical method is related to the calculation of the Lyapunov characteristic exponents (LCEs). Usually, to implement the classical algorithms for the LCEs calculation, the smoothness of the right-hand sides of the corresponding equations is required. In this work, we propose a new algorithm for the LCEs computation in systems with strong nonlinearities (these nonlinearities cannot be linearized) including the hysteresis. This algorithm uses the values of the Jacobi matrix in the vicinity of singularities of the right-hand sides of the corresponding equations. The proposed modification of the algorithm is also can be used for systems containing such design hysteresis nonlinearity as the Preisach operator. (Thus, this modification can be used for all members of the hysteresis family.) Moreover, the proposed algorithm can be successfully applied to the well-known chaotic systems with smooth nonlinearities. Examples of dynamical systems with hysteresis nonlinearities, such as the Lorentz system with hysteresis friction and the van der Pol oscillator with hysteresis block, are considered. These examples illustrate the efficiency of the proposed algorithm. © The Author(s), under exclusive licence to Springer Nature B.V. 2022
abstract_unstemmed	Abstract One of the most important problems of nonlinear dynamics is related to the development of methods concerning the identification of the dynamical modes of the corresponding systems. The classical method is related to the calculation of the Lyapunov characteristic exponents (LCEs). Usually, to implement the classical algorithms for the LCEs calculation, the smoothness of the right-hand sides of the corresponding equations is required. In this work, we propose a new algorithm for the LCEs computation in systems with strong nonlinearities (these nonlinearities cannot be linearized) including the hysteresis. This algorithm uses the values of the Jacobi matrix in the vicinity of singularities of the right-hand sides of the corresponding equations. The proposed modification of the algorithm is also can be used for systems containing such design hysteresis nonlinearity as the Preisach operator. (Thus, this modification can be used for all members of the hysteresis family.) Moreover, the proposed algorithm can be successfully applied to the well-known chaotic systems with smooth nonlinearities. Examples of dynamical systems with hysteresis nonlinearities, such as the Lorentz system with hysteresis friction and the van der Pol oscillator with hysteresis block, are considered. These examples illustrate the efficiency of the proposed algorithm. © The Author(s), under exclusive licence to Springer Nature B.V. 2022
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title_short	A new way to compute the Lyapunov characteristic exponents for non-smooth and discontinues dynamical systems
url	https://dx.doi.org/10.1007/s11071-022-07492-6
remote_bool	true
author2	Borzunov, Sergei V. Meleshenko, Peter A.
author2Str	Borzunov, Sergei V. Meleshenko, Peter A.
ppnlink	315297034
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doi_str	10.1007/s11071-022-07492-6
up_date	2024-07-03T15:01:09.507Z
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A new way to compute the Lyapunov characteristic exponents for non-smooth and discontinues dynamical systems

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