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AuthorVijayakumar, M. D.
AuthorNatiq, Hayder
AuthorLeutcho, Gervais Dolvis
AuthorRajagopal, Karthikeyan
AuthorJafari, Sajad
AuthorHussain, Iqtadar
Available date2022-05-30T06:50:38Z
Publication Date2022-04-01
Publication NameInternational Journal of Bifurcation and Chaos
Identifierhttp://dx.doi.org/10.1142/S0218127422500638
CitationVijayakumar, M. D., Hayder Natiq, Gervais Dolvis Leutcho, Karthikeyan Rajagopal, Sajad Jafari, and Iqtadar Hussain. "Hidden and Self-Excited Collective Dynamics of a New Multistable Hyper-Jerk System with Unique Equilibrium." International Journal of Bifurcation and Chaos 32, no. 05 (2022): 2250063.
ISSN02181274
URIhttps://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=85129247823&origin=inward
URIhttp://hdl.handle.net/10576/31647
AbstractNonlinear dynamical systems with hidden attractors belong to a recent and hot area of research. Such systems can exist in different forms, such as without equilibrium or with a stable equilibrium point. This paper focuses on the dynamics of a new 4D chaotic hyper-jerk system with a unique equilibrium point. It is shown that the new hyper-jerk system effectively exhibits different hidden behaviors, which are hidden point attractor, hidden periodic attractor, and hidden chaotic state. Collective behaviors of the system are studied in terms of the equilibrium point, bifurcation diagrams, phase portraits, frequency spectra, and two-parameter Lyapunov exponents. Some remarkable and exciting properties are found in the new snap system, such as period-doubling transition, asymmetric bubbles, and coexisting bifurcations. Also, we demonstrate that it is possible to generate different varieties of two, three, four, or five coexisting hidden and self-excited attractors in the introduced model. In addition, the amplitude and offset of the hidden chaotic attractors are perfectly controlled for possible application in engineering. Furthermore, a circuit design has been implemented to support the physical feasibility of the proposed model.
SponsorThis work is partially funded by Center for Materials Research, Chennai Institute of Technology, Chennai, India via funding number CIT/CMR/2021/RD/003.
Languageen
Subjectcontrol
hidden attractor
Hyper-jerk system
multistability
stable equilibrium
TitleHidden and Self-Excited Collective Dynamics of a New Multistable Hyper-Jerk System with Unique Equilibrium
TypeArticle
Issue Number5
Volume Number32
ESSN1793-6551


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