Dynamical analysis and adaptive synchronization of a new 6D hyperchaotic system with the cosine function.
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| Title: | Dynamical analysis and adaptive synchronization of a new 6D hyperchaotic system with the cosine function. |
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| Authors: | Kopp, Michael1, Samuilik, Inna2,3 Inna.Samuilika@rtu.lv |
| Source: | Mathematical Modelling & Analysis. 2025, Vol. 30 Issue 4, p626-644. 19p. |
| Subjects: | Synchronization, Cosine function, Lyapunov exponents, Dynamical systems, Lorenz equations, Dynamic stability, Bifurcation diagrams |
| Abstract: | This paper presents a novel 6D dynamic system derived from modified second-type 3D Lorenz equations using state feedback control. While these original 3D equations are structurally simpler than the classical Lorenz equations, they generate more topologically complex attractors with a distinctive two-winged butterfly structure. The proposed system is the most compact of its kind in the literature, containing only 11 terms: two cross-product nonlinearities, two piecewise linear functions, one cosine function, five linear terms, and one constant. The newly developed 6D hyperchaotic system exhibits rich dynamic properties, including hidden attractors and dissipative behavior. A detailed dynamic analysis has identified two unstable hyperbolic equilibrium points, indicating the potential for self-exciting attractors. Additionally, bifurcation diagrams were constructed, Lyapunov exponents were computed, and the maximum Kaplan-Yorke dimension DKY = 3.23 was obtained at parameter value a = 0.5, revealing the high complexity of the hyperchaotic dynamics. Furthermore, multistability and offset boosting control were examined to gain deeper insights into the system's behavior. Finally, synchronization between two identical 6D hyperchaotic systems was successfully achieved using an adaptive control method. [ABSTRACT FROM AUTHOR] |
| Copyright of Mathematical Modelling & Analysis is the property of Vilnius Gediminas Technical University and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Header | DbId: egs DbLabel: Engineering Source An: 189276565 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Dynamical analysis and adaptive synchronization of a new 6D hyperchaotic system with the cosine function. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Kopp%2C+Michael%22">Kopp, Michael</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Samuilik%2C+Inna%22">Samuilik, Inna</searchLink><relatesTo>2,3</relatesTo><i> Inna.Samuilika@rtu.lv</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Mathematical+Modelling+%26+Analysis%22">Mathematical Modelling & Analysis</searchLink>. 2025, Vol. 30 Issue 4, p626-644. 19p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Synchronization%22">Synchronization</searchLink><br /><searchLink fieldCode="DE" term="%22Cosine+function%22">Cosine function</searchLink><br /><searchLink fieldCode="DE" term="%22Lyapunov+exponents%22">Lyapunov exponents</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamical+systems%22">Dynamical systems</searchLink><br /><searchLink fieldCode="DE" term="%22Lorenz+equations%22">Lorenz equations</searchLink><br /><searchLink fieldCode="DE" term="%22Dynamic+stability%22">Dynamic stability</searchLink><br /><searchLink fieldCode="DE" term="%22Bifurcation+diagrams%22">Bifurcation diagrams</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: This paper presents a novel 6D dynamic system derived from modified second-type 3D Lorenz equations using state feedback control. While these original 3D equations are structurally simpler than the classical Lorenz equations, they generate more topologically complex attractors with a distinctive two-winged butterfly structure. The proposed system is the most compact of its kind in the literature, containing only 11 terms: two cross-product nonlinearities, two piecewise linear functions, one cosine function, five linear terms, and one constant. The newly developed 6D hyperchaotic system exhibits rich dynamic properties, including hidden attractors and dissipative behavior. A detailed dynamic analysis has identified two unstable hyperbolic equilibrium points, indicating the potential for self-exciting attractors. Additionally, bifurcation diagrams were constructed, Lyapunov exponents were computed, and the maximum Kaplan-Yorke dimension DKY = 3.23 was obtained at parameter value a = 0.5, revealing the high complexity of the hyperchaotic dynamics. Furthermore, multistability and offset boosting control were examined to gain deeper insights into the system's behavior. Finally, synchronization between two identical 6D hyperchaotic systems was successfully achieved using an adaptive control method. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Mathematical Modelling & Analysis is the property of Vilnius Gediminas Technical University and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.3846/mma.2025.23438 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 19 StartPage: 626 Subjects: – SubjectFull: Synchronization Type: general – SubjectFull: Cosine function Type: general – SubjectFull: Lyapunov exponents Type: general – SubjectFull: Dynamical systems Type: general – SubjectFull: Lorenz equations Type: general – SubjectFull: Dynamic stability Type: general – SubjectFull: Bifurcation diagrams Type: general Titles: – TitleFull: Dynamical analysis and adaptive synchronization of a new 6D hyperchaotic system with the cosine function. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Kopp, Michael – PersonEntity: Name: NameFull: Samuilik, Inna IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 10 Text: 2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 13926292 Numbering: – Type: volume Value: 30 – Type: issue Value: 4 Titles: – TitleFull: Mathematical Modelling & Analysis Type: main |
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