Assessing the Non-Linear Dynamics of a Hopf–Langford Type System
In this paper, the non-linear dynamical behavior of a 3D autonomous dissipative system of Hopf–Langford type is investigated. Through the help of a mode transformation (as the system’s energy is included) it is shown that the 3D nonlinear system can be separated of two coupled subsystems in the mast...
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MDPI AG
2021-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/9/18/2340 |
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doaj-0d699ceca5894a9e9bc170a1340be8522021-09-26T00:38:45ZengMDPI AGMathematics2227-73902021-09-0192340234010.3390/math9182340Assessing the Non-Linear Dynamics of a Hopf–Langford Type SystemSvetoslav G. Nikolov0Vassil M. Vassilev1Institute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., bl. 4, 1113 Sofia, BulgariaInstitute of Mechanics, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., bl. 4, 1113 Sofia, BulgariaIn this paper, the non-linear dynamical behavior of a 3D autonomous dissipative system of Hopf–Langford type is investigated. Through the help of a mode transformation (as the system’s energy is included) it is shown that the 3D nonlinear system can be separated of two coupled subsystems in the master (drive)-slave (response) synchronization type. After that, based on the computing first and second Lyapunov values for master system, we have attempted to give a general framework (from bifurcation theory point of view) for understanding the structural stability and bifurcation behavior of original system. Moreover, a family of exact solutions of the master system is obtained and discussed. The effect of synchronization on the dynamic behavior of original system is also studied by numerical simulations.https://www.mdpi.com/2227-7390/9/18/2340analysissynchronizationnonlinear dynamicsHopf–Langford system |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Svetoslav G. Nikolov Vassil M. Vassilev |
| spellingShingle |
Svetoslav G. Nikolov Vassil M. Vassilev Assessing the Non-Linear Dynamics of a Hopf–Langford Type System Mathematics analysis synchronization nonlinear dynamics Hopf–Langford system |
| author_facet |
Svetoslav G. Nikolov Vassil M. Vassilev |
| author_sort |
Svetoslav G. Nikolov |
| title |
Assessing the Non-Linear Dynamics of a Hopf–Langford Type System |
| title_short |
Assessing the Non-Linear Dynamics of a Hopf–Langford Type System |
| title_full |
Assessing the Non-Linear Dynamics of a Hopf–Langford Type System |
| title_fullStr |
Assessing the Non-Linear Dynamics of a Hopf–Langford Type System |
| title_full_unstemmed |
Assessing the Non-Linear Dynamics of a Hopf–Langford Type System |
| title_sort |
assessing the non-linear dynamics of a hopf–langford type system |
| publisher |
MDPI AG |
| series |
Mathematics |
| issn |
2227-7390 |
| publishDate |
2021-09-01 |
| description |
In this paper, the non-linear dynamical behavior of a 3D autonomous dissipative system of Hopf–Langford type is investigated. Through the help of a mode transformation (as the system’s energy is included) it is shown that the 3D nonlinear system can be separated of two coupled subsystems in the master (drive)-slave (response) synchronization type. After that, based on the computing first and second Lyapunov values for master system, we have attempted to give a general framework (from bifurcation theory point of view) for understanding the structural stability and bifurcation behavior of original system. Moreover, a family of exact solutions of the master system is obtained and discussed. The effect of synchronization on the dynamic behavior of original system is also studied by numerical simulations. |
| topic |
analysis synchronization nonlinear dynamics Hopf–Langford system |
| url |
https://www.mdpi.com/2227-7390/9/18/2340 |
| work_keys_str_mv |
AT svetoslavgnikolov assessingthenonlineardynamicsofahopflangfordtypesystem AT vassilmvassilev assessingthenonlineardynamicsofahopflangfordtypesystem |
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1716870141190340608 |