Bursting behaviour control based on low-frequency amplitude-modulated excitation in a hybrid van der Pol–Rayleigh oscillator.
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| Title: | Bursting behaviour control based on low-frequency amplitude-modulated excitation in a hybrid van der Pol–Rayleigh oscillator. |
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| Authors: | Zhang, Zhen-Zhen1 (AUTHOR), Ma, Xin-Dong2 (AUTHOR) 1000004942@ujs.edu.cn |
| Source: | Pramana: Journal of Physics. Jun2026, Vol. 100 Issue 2, p1-13. 13p. |
| Subjects: | Relaxation oscillators, Nonlinear oscillators, Hopf bifurcations, Bifurcation theory, Nonlinear mechanics, Singular perturbations |
| Abstract: | Understanding the generative mechanisms and evolutionary laws of bursting behaviours, as well as developing effective strategies for encouraging or suppressing bursting, is an important topic in nonlinear dynamics. In the present work, we pay close attention to the impact of the slow-changing amplitude-modulated excitation (AME) on the dynamic behaviours in a hybrid van der Pol–Rayleigh oscillator. Typically, two symmetric pulse-shaped explosion (PSE)-type bursting behaviours, i.e., symmetric relaxation oscillation and symmetric Hopf/Hopf-Hopf/Hopf bursting, can be exhibited in the unmodulated system. We demonstrate that the AME can significantly alter the symmetry and bifurcation structures of the system. Consequently, the AME can induce the generation of new asymmetric bursting behaviours. Specifically, the symmetric relaxation oscillation can be modulated into two different dynamic behaviours, namely asymmetric relaxation oscillation and asymmetric Hopf/Hopf bursting and the symmetric Hopf/Hopf–Hopf/Hopf bursting are modulated into two different bursting patterns called asymmetric Hopf/Hopf bursting and asymmetric Hopf/Hopf–Hopf/Hopf bursting. We explore the mechanism of the bursting behaviours of the amplitude-modulated system by the slow–fast dynamic analysis. The results indicate that the AME is a valuable method for encouraging or suppressing the generation of bursting behaviours and it has specific theoretical and engineering value for controlling the system's dynamic behaviours. [ABSTRACT FROM AUTHOR] |
| Copyright of Pramana: Journal of Physics is the property of Springer Nature 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: 193389898 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Bursting behaviour control based on low-frequency amplitude-modulated excitation in a hybrid van der Pol–Rayleigh oscillator. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Zhang%2C+Zhen-Zhen%22">Zhang, Zhen-Zhen</searchLink><relatesTo>1</relatesTo> (AUTHOR)<br /><searchLink fieldCode="AR" term="%22Ma%2C+Xin-Dong%22">Ma, Xin-Dong</searchLink><relatesTo>2</relatesTo> (AUTHOR)<i> 1000004942@ujs.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Pramana%3A+Journal+of+Physics%22">Pramana: Journal of Physics</searchLink>. Jun2026, Vol. 100 Issue 2, p1-13. 13p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Relaxation+oscillators%22">Relaxation oscillators</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+oscillators%22">Nonlinear oscillators</searchLink><br /><searchLink fieldCode="DE" term="%22Hopf+bifurcations%22">Hopf bifurcations</searchLink><br /><searchLink fieldCode="DE" term="%22Bifurcation+theory%22">Bifurcation theory</searchLink><br /><searchLink fieldCode="DE" term="%22Nonlinear+mechanics%22">Nonlinear mechanics</searchLink><br /><searchLink fieldCode="DE" term="%22Singular+perturbations%22">Singular perturbations</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Understanding the generative mechanisms and evolutionary laws of bursting behaviours, as well as developing effective strategies for encouraging or suppressing bursting, is an important topic in nonlinear dynamics. In the present work, we pay close attention to the impact of the slow-changing amplitude-modulated excitation (AME) on the dynamic behaviours in a hybrid van der Pol–Rayleigh oscillator. Typically, two symmetric pulse-shaped explosion (PSE)-type bursting behaviours, i.e., symmetric relaxation oscillation and symmetric Hopf/Hopf-Hopf/Hopf bursting, can be exhibited in the unmodulated system. We demonstrate that the AME can significantly alter the symmetry and bifurcation structures of the system. Consequently, the AME can induce the generation of new asymmetric bursting behaviours. Specifically, the symmetric relaxation oscillation can be modulated into two different dynamic behaviours, namely asymmetric relaxation oscillation and asymmetric Hopf/Hopf bursting and the symmetric Hopf/Hopf–Hopf/Hopf bursting are modulated into two different bursting patterns called asymmetric Hopf/Hopf bursting and asymmetric Hopf/Hopf–Hopf/Hopf bursting. We explore the mechanism of the bursting behaviours of the amplitude-modulated system by the slow–fast dynamic analysis. The results indicate that the AME is a valuable method for encouraging or suppressing the generation of bursting behaviours and it has specific theoretical and engineering value for controlling the system's dynamic behaviours. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Pramana: Journal of Physics is the property of Springer Nature 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.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=egs&AN=193389898 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s12043-025-03093-1 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 13 StartPage: 1 Subjects: – SubjectFull: Relaxation oscillators Type: general – SubjectFull: Nonlinear oscillators Type: general – SubjectFull: Hopf bifurcations Type: general – SubjectFull: Bifurcation theory Type: general – SubjectFull: Nonlinear mechanics Type: general – SubjectFull: Singular perturbations Type: general Titles: – TitleFull: Bursting behaviour control based on low-frequency amplitude-modulated excitation in a hybrid van der Pol–Rayleigh oscillator. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Zhang, Zhen-Zhen – PersonEntity: Name: NameFull: Ma, Xin-Dong IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 06 Text: Jun2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 03044289 Numbering: – Type: volume Value: 100 – Type: issue Value: 2 Titles: – TitleFull: Pramana: Journal of Physics Type: main |
| ResultId | 1 |
