Analysis of the Dynamics of a $\phi^{6}$ Duffing Type Jerk System
A theoretically and numerically analysis on Duffing Jerk systems with a sixth-order type potential and a sixth-order potential smoothed by a gaussian function are carried out in this work. The Jerk is transformed into a dynamical system of dimension three. The dynamics and stability of the resulting...
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| Format: | Article |
| Language: | English |
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Akif AKGUL
2024-06-01
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| Series: | Chaos Theory and Applications |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/3476852 |
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| author | Ulises Uriostegui-legorreta Eduardo Salvador Tututi-hernández Alejandro Bucio |
| author_facet | Ulises Uriostegui-legorreta Eduardo Salvador Tututi-hernández Alejandro Bucio |
| author_sort | Ulises Uriostegui-legorreta |
| collection | DOAJ |
| description | A theoretically and numerically analysis on Duffing Jerk systems with a sixth-order type potential and a sixth-order potential smoothed by a gaussian function are carried out in this work. The Jerk is transformed into a dynamical system of dimension three. The dynamics and stability of the resulting system are analyzed, through phase space, bifurcation diagrams and Lyapunov exponents by varying the relevant parameters, finding the existence of a strange attractor. The dynamics of system with potential smoothed was studied by varying the smoothing parameter $\alpha$, finding that this parameter can be used to controlling chaos, since the exponential factor keeps the same fixed points and it regulates smoothly the amplitude of the potential. |
| format | Article |
| id | doaj-art-c3d290776c744ebeb5c013592ec487d2 |
| institution | Kabale University |
| issn | 2687-4539 |
| language | English |
| publishDate | 2024-06-01 |
| publisher | Akif AKGUL |
| record_format | Article |
| series | Chaos Theory and Applications |
| spelling | doaj-art-c3d290776c744ebeb5c013592ec487d22025-01-23T18:19:49ZengAkif AKGULChaos Theory and Applications2687-45392024-06-0162838910.51537/chaos.13764711971Analysis of the Dynamics of a $\phi^{6}$ Duffing Type Jerk SystemUlises Uriostegui-legorreta0https://orcid.org/0000-0001-9905-6060Eduardo Salvador Tututi-hernández1https://orcid.org/0000-0002-0126-6615Alejandro Bucio2https://orcid.org/0009-0000-3295-4157Universidad Michoacana de San Nicolás de HidalgoUniversidad Michoacana de San Nicolás de HidalgoUniversidad Michoacana de San Nicolás de HidalgoA theoretically and numerically analysis on Duffing Jerk systems with a sixth-order type potential and a sixth-order potential smoothed by a gaussian function are carried out in this work. The Jerk is transformed into a dynamical system of dimension three. The dynamics and stability of the resulting system are analyzed, through phase space, bifurcation diagrams and Lyapunov exponents by varying the relevant parameters, finding the existence of a strange attractor. The dynamics of system with potential smoothed was studied by varying the smoothing parameter $\alpha$, finding that this parameter can be used to controlling chaos, since the exponential factor keeps the same fixed points and it regulates smoothly the amplitude of the potential.https://dergipark.org.tr/en/download/article-file/3476852jerk systemduffing systembifurcation diagramslyapunov exponent |
| spellingShingle | Ulises Uriostegui-legorreta Eduardo Salvador Tututi-hernández Alejandro Bucio Analysis of the Dynamics of a $\phi^{6}$ Duffing Type Jerk System Chaos Theory and Applications jerk system duffing system bifurcation diagrams lyapunov exponent |
| title | Analysis of the Dynamics of a $\phi^{6}$ Duffing Type Jerk System |
| title_full | Analysis of the Dynamics of a $\phi^{6}$ Duffing Type Jerk System |
| title_fullStr | Analysis of the Dynamics of a $\phi^{6}$ Duffing Type Jerk System |
| title_full_unstemmed | Analysis of the Dynamics of a $\phi^{6}$ Duffing Type Jerk System |
| title_short | Analysis of the Dynamics of a $\phi^{6}$ Duffing Type Jerk System |
| title_sort | analysis of the dynamics of a phi 6 duffing type jerk system |
| topic | jerk system duffing system bifurcation diagrams lyapunov exponent |
| url | https://dergipark.org.tr/en/download/article-file/3476852 |
| work_keys_str_mv | AT ulisesuriosteguilegorreta analysisofthedynamicsofaphi6duffingtypejerksystem AT eduardosalvadortututihernandez analysisofthedynamicsofaphi6duffingtypejerksystem AT alejandrobucio analysisofthedynamicsofaphi6duffingtypejerksystem |