A New 6D Two-wing Hyperchaotic System: Dynamical Analysis, Circuit Design, and Sinchronization
This paper introduces a novel 6D dynamic system derived from modified 3D Lorenz equations of the second type using state feedback control. While the original 3D equations are formally simpler than the classical Lorentz equations, they produce topologically more complex attractors with a two-winged b...
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| Language: | English |
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Akif AKGUL
2024-11-01
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| Series: | Chaos Theory and Applications |
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| Online Access: | https://dergipark.org.tr/en/download/article-file/4056938 |
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| author | Michael Kopp Inna Samuilik |
| author_facet | Michael Kopp Inna Samuilik |
| author_sort | Michael Kopp |
| collection | DOAJ |
| description | This paper introduces a novel 6D dynamic system derived from modified 3D Lorenz equations of the second type using state feedback control. While the original 3D equations are formally simpler than the classical Lorentz equations, they produce topologically more complex attractors with a two-winged butterfly structure. The proposed system contains the fewest terms compared to existing literature. These terms comprise two cross-product nonlinearities, two piecewise linear functions, six linear terms, and one constant. The new 6D hyperchaotic system exhibits a rich array of dynamic characteristics, including hidden attractors and dissipative behavior. A thorough dynamic analysis of this system was performed. In particular, bifurcation diagrams were constructed, Lyapunov exponents and dimensions were calculated, and multistability and offset boosting control were analyzed to understand the systems behavior further. An electronic circuit of the 6D hyperchaotic two-winged butterfly system was developed in the Multisim computer environment. The designed electronic circuit showed excellent agreement with the simulation results of the new 6D dynamic system. Synchronization of two identical 6D hyperchaotic systems was achieved using the active control method. |
| format | Article |
| id | doaj-art-e0bc04c986bd41a3802e3bd77213f6ea |
| institution | Kabale University |
| issn | 2687-4539 |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Akif AKGUL |
| record_format | Article |
| series | Chaos Theory and Applications |
| spelling | doaj-art-e0bc04c986bd41a3802e3bd77213f6ea2025-01-23T18:18:48ZengAkif AKGULChaos Theory and Applications2687-45392024-11-016427328310.51537/chaos.15130801971A New 6D Two-wing Hyperchaotic System: Dynamical Analysis, Circuit Design, and SinchronizationMichael Kopp0https://orcid.org/0000-0001-7457-3272Inna Samuilik1https://orcid.org/0000-0002-8892-5715Institute for Single CrystalsRiga Technical UniversityThis paper introduces a novel 6D dynamic system derived from modified 3D Lorenz equations of the second type using state feedback control. While the original 3D equations are formally simpler than the classical Lorentz equations, they produce topologically more complex attractors with a two-winged butterfly structure. The proposed system contains the fewest terms compared to existing literature. These terms comprise two cross-product nonlinearities, two piecewise linear functions, six linear terms, and one constant. The new 6D hyperchaotic system exhibits a rich array of dynamic characteristics, including hidden attractors and dissipative behavior. A thorough dynamic analysis of this system was performed. In particular, bifurcation diagrams were constructed, Lyapunov exponents and dimensions were calculated, and multistability and offset boosting control were analyzed to understand the systems behavior further. An electronic circuit of the 6D hyperchaotic two-winged butterfly system was developed in the Multisim computer environment. The designed electronic circuit showed excellent agreement with the simulation results of the new 6D dynamic system. Synchronization of two identical 6D hyperchaotic systems was achieved using the active control method.https://dergipark.org.tr/en/download/article-file/4056938two-wing attractorschaotic behaviormultistabilityoffset boosting controlcircuit implementationactive control synchronization |
| spellingShingle | Michael Kopp Inna Samuilik A New 6D Two-wing Hyperchaotic System: Dynamical Analysis, Circuit Design, and Sinchronization Chaos Theory and Applications two-wing attractors chaotic behavior multistability offset boosting control circuit implementation active control synchronization |
| title | A New 6D Two-wing Hyperchaotic System: Dynamical Analysis, Circuit Design, and Sinchronization |
| title_full | A New 6D Two-wing Hyperchaotic System: Dynamical Analysis, Circuit Design, and Sinchronization |
| title_fullStr | A New 6D Two-wing Hyperchaotic System: Dynamical Analysis, Circuit Design, and Sinchronization |
| title_full_unstemmed | A New 6D Two-wing Hyperchaotic System: Dynamical Analysis, Circuit Design, and Sinchronization |
| title_short | A New 6D Two-wing Hyperchaotic System: Dynamical Analysis, Circuit Design, and Sinchronization |
| title_sort | new 6d two wing hyperchaotic system dynamical analysis circuit design and sinchronization |
| topic | two-wing attractors chaotic behavior multistability offset boosting control circuit implementation active control synchronization |
| url | https://dergipark.org.tr/en/download/article-file/4056938 |
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