Deterministic chaos in pendulum systems with delay
Dynamic system "pendulum - source of limited excitation" with taking into account the various factors of delay is considered. Mathematical model of the system is a system of ordinary differential equations with delay. Three approaches are suggested that allow to reduce the mathematical mod...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Sciendo
2019-02-01
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| Series: | Applied Mathematics and Nonlinear Sciences |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/AMNS.2019.1.00001 |
| _version_ | 1797219134018158592 |
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| author | Shvets Aleksandr Makaseyev Alexander |
| author_facet | Shvets Aleksandr Makaseyev Alexander |
| author_sort | Shvets Aleksandr |
| collection | DOAJ |
| description | Dynamic system "pendulum - source of limited excitation" with taking into account the various factors of delay is considered. Mathematical model of the system is a system of ordinary differential equations with delay. Three approaches are suggested that allow to reduce the mathematical model of the system to systems of differential equations, into which various factors of delay enter as some parameters. Genesis of deterministic chaos is studied in detail. Maps of dynamic regimes, phase-portraits of attractors of systems, phase-parametric characteristics and Lyapunov characteristic exponents are constructed and analyzed. The scenarios of transition from steady-state regular regimes to chaotic ones are identified. It is shown, that in some cases the delay is the main reason of origination of chaos in the system "pendulum - source of limited excitation". |
| first_indexed | 2024-04-24T12:28:49Z |
| format | Article |
| id | doaj.art-a792b84d9202468aac0d965b58b336c5 |
| institution | Directory Open Access Journal |
| issn | 2444-8656 |
| language | English |
| last_indexed | 2024-04-24T12:28:49Z |
| publishDate | 2019-02-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Applied Mathematics and Nonlinear Sciences |
| spelling | doaj.art-a792b84d9202468aac0d965b58b336c52024-04-08T07:36:49ZengSciendoApplied Mathematics and Nonlinear Sciences2444-86562019-02-01411810.2478/AMNS.2019.1.00001Deterministic chaos in pendulum systems with delayShvets Aleksandr0Makaseyev Alexander1National Technical University Of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kiev, UkraineNational Technical University Of Ukraine "Igor Sikorsky Kyiv Polytechnic Institute", Kiev, UkraineDynamic system "pendulum - source of limited excitation" with taking into account the various factors of delay is considered. Mathematical model of the system is a system of ordinary differential equations with delay. Three approaches are suggested that allow to reduce the mathematical model of the system to systems of differential equations, into which various factors of delay enter as some parameters. Genesis of deterministic chaos is studied in detail. Maps of dynamic regimes, phase-portraits of attractors of systems, phase-parametric characteristics and Lyapunov characteristic exponents are constructed and analyzed. The scenarios of transition from steady-state regular regimes to chaotic ones are identified. It is shown, that in some cases the delay is the main reason of origination of chaos in the system "pendulum - source of limited excitation".https://doi.org/10.2478/AMNS.2019.1.00001chaotic attractorsystem with limited excitationfactors of delay34c1537d45 |
| spellingShingle | Shvets Aleksandr Makaseyev Alexander Deterministic chaos in pendulum systems with delay Applied Mathematics and Nonlinear Sciences chaotic attractor system with limited excitation factors of delay 34c15 37d45 |
| title | Deterministic chaos in pendulum systems with delay |
| title_full | Deterministic chaos in pendulum systems with delay |
| title_fullStr | Deterministic chaos in pendulum systems with delay |
| title_full_unstemmed | Deterministic chaos in pendulum systems with delay |
| title_short | Deterministic chaos in pendulum systems with delay |
| title_sort | deterministic chaos in pendulum systems with delay |
| topic | chaotic attractor system with limited excitation factors of delay 34c15 37d45 |
| url | https://doi.org/10.2478/AMNS.2019.1.00001 |
| work_keys_str_mv | AT shvetsaleksandr deterministicchaosinpendulumsystemswithdelay AT makaseyevalexander deterministicchaosinpendulumsystemswithdelay |