A comparative study of the dynamics of a three-disk dynamo system with and without time delay

Deng, S; Ji, J; Wen, G; Xu, H

A comparative study of the dynamics of a three-disk dynamo system with and without time delay

Deng, S Ji, J

Wen, G Xu, H

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Publisher:: ELSEVIER SCIENCE INC
Publication Type:: Journal Article
Citation:: Applied Mathematics and Computation, 2021, 399
Issue Date:: 2021-06-15

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Field	Value	Language
dc.contributor.author	Deng, S
dc.contributor.author	Ji, J https://orcid.org/0000-0003-3280-5463
dc.contributor.author	Wen, G
dc.contributor.author	Xu, H
dc.date.accessioned	2021-05-16T11:50:20Z
dc.date.available	2021-05-16T11:50:20Z
dc.date.issued	2021-06-15
dc.identifier.citation	Applied Mathematics and Computation, 2021, 399
dc.identifier.issn	0096-3003
dc.identifier.issn	1873-5649
dc.identifier.uri	http://hdl.handle.net/10453/148912
dc.description.abstract	The disk dynamo plays an important role in studying the geodynamo and much research works have been devoted to the understanding of dynamo dynamics. This paper further investigates an extended disk dynamo system having three coupled conducting disks and incorporates the interaction-induced time delay in the dynamic governing equations. By carrying out a comparative analysis, the dynamic behaviors of the coupled three-disk dynamo system with and without time delay are studied to explore novel and complex nonlinear dynamic phenomena in the coupled delayed dynamo system. It is found that the double Hopf bifurcations can be induced in the time-delayed dynamo system. Three different topological structures of the unfolding are obtained under different time delays. Accordingly, it is shown that the novel dynamic behaviors, including quasi-periodic torus, three-dimensional torus and the coexistence of multiple attractors, can appear in the time-delayed dynamo system. Furthermore, by performing the continuation analysis on the periodic orbit generated from the Hopf bifurcation of equilibrium, some new coexistence patterns, e.g., the coexistence of periodic orbits and chaos, the coexistence of quasi-periodic orbits and chaos, are observed in the dynamo system with time delay. Based on the obtained results, it is believed that the inclusion of time delay in the modelling of the three-disk dynamo system is necessary and meaningful for developing an in-depth understanding of dynamo dynamics. Finally, the results of theoretical analyses are verified by the numerical simulations.
dc.language	English
dc.publisher	ELSEVIER SCIENCE INC
dc.relation.ispartof	Applied Mathematics and Computation
dc.relation.isbasedon	10.1016/j.amc.2021.126016
dc.rights	info:eu-repo/semantics/embargoedAccess
dc.subject	0102 Applied Mathematics, 0103 Numerical and Computational Mathematics, 0802 Computation Theory and Mathematics
dc.subject.classification	Numerical & Computational Mathematics
dc.title	A comparative study of the dynamics of a three-disk dynamo system with and without time delay
dc.type	Journal Article
utslib.citation.volume	399
utslib.for	0102 Applied Mathematics
utslib.for	0103 Numerical and Computational Mathematics
utslib.for	0802 Computation Theory and Mathematics
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Mechanical and Mechatronic Engineering
utslib.copyright.status	open_access	*
utslib.copyright.embargo	2022-06-15T00:00:00+1000Z
dc.date.updated	2021-05-16T11:50:12Z
pubs.publication-status	Accepted
pubs.volume	399

Abstract:

The disk dynamo plays an important role in studying the geodynamo and much research works have been devoted to the understanding of dynamo dynamics. This paper further investigates an extended disk dynamo system having three coupled conducting disks and incorporates the interaction-induced time delay in the dynamic governing equations. By carrying out a comparative analysis, the dynamic behaviors of the coupled three-disk dynamo system with and without time delay are studied to explore novel and complex nonlinear dynamic phenomena in the coupled delayed dynamo system. It is found that the double Hopf bifurcations can be induced in the time-delayed dynamo system. Three different topological structures of the unfolding are obtained under different time delays. Accordingly, it is shown that the novel dynamic behaviors, including quasi-periodic torus, three-dimensional torus and the coexistence of multiple attractors, can appear in the time-delayed dynamo system. Furthermore, by performing the continuation analysis on the periodic orbit generated from the Hopf bifurcation of equilibrium, some new coexistence patterns, e.g., the coexistence of periodic orbits and chaos, the coexistence of quasi-periodic orbits and chaos, are observed in the dynamo system with time delay. Based on the obtained results, it is believed that the inclusion of time delay in the modelling of the three-disk dynamo system is necessary and meaningful for developing an in-depth understanding of dynamo dynamics. Finally, the results of theoretical analyses are verified by the numerical simulations.

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http://hdl.handle.net/10453/148912