Network Dynamics of a Fractional-Order Phase-Locked Loop with Infinite Coexisting Attractors
Joint Authors
Karthikeyan, Anitha
Rajagopal, Karthikeyan
Source
Issue
Vol. 2020, Issue 2020 (31 Dec. 2020), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2020-09-02
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
We have investigated a fractional-order phase-locked loop characterised by a third-order differential equation.
The integer-order mathematical model of the phase-locked loop (PLL) is first converted to fractional order using the Caputo-Fabrizio method.
The stability of the equilibrium points is discussed in detail in both parameter and fractional-order domain.
The proposed fractional-order phase-locked loop (FOPLL) model shows multiple coexisting attractors which was not discussed in the earlier literature of PLL.
The significance of these infinite coexisting attractors is that they exist in the operation region of the PLL between [−π,π] which increases the complexity of operation of the PLLs.
Mainly when such FOPLLs are used in large-scale networks, the synchronisation of the FOPLLs becomes complicated and will result in unstable control conditions.
Hence, studying the network dynamics of such FOPLLs is significant which motivates us to investigate the synchronisation phenomenon of the FOPLLs constructed in a square network.
We could show that, because of the multiple coexisting attractors, the FOPLLs show various synchronisation phenomena, and more importantly in the chaotic region for lower fractional-order values, we could show that the FOPLLs are synchronised and this finding is very useful to completely analyse the FOPLL networks in high-frequency operations.
American Psychological Association (APA)
Karthikeyan, Anitha& Rajagopal, Karthikeyan. 2020. Network Dynamics of a Fractional-Order Phase-Locked Loop with Infinite Coexisting Attractors. Complexity،Vol. 2020, no. 2020, pp.1-11.
https://search.emarefa.net/detail/BIM-1143948
Modern Language Association (MLA)
Karthikeyan, Anitha& Rajagopal, Karthikeyan. Network Dynamics of a Fractional-Order Phase-Locked Loop with Infinite Coexisting Attractors. Complexity No. 2020 (2020), pp.1-11.
https://search.emarefa.net/detail/BIM-1143948
American Medical Association (AMA)
Karthikeyan, Anitha& Rajagopal, Karthikeyan. Network Dynamics of a Fractional-Order Phase-Locked Loop with Infinite Coexisting Attractors. Complexity. 2020. Vol. 2020, no. 2020, pp.1-11.
https://search.emarefa.net/detail/BIM-1143948
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1143948