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Hopf Bifurcation, Positively Invariant Set, and Physical Realization of a New Four-Dimensional Hyperchaotic Financial System
Joint Authors
Zhang, Wei
Akgul, Akif
Wei, Zhouchao
Kai, G.
Wang, J. F.
Source
Mathematical Problems in Engineering
Issue
Vol. 2017, Issue 2017 (31 Dec. 2017), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2017-04-10
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
This paper introduces a new four-dimensional hyperchaotic financial system on the basis of an established three-dimensional nonlinear financial system and a dynamic model by adding a controller term to consider the effect of control on the system.
In terms of the proposed financial system, the sufficient conditions for nonexistence of chaotic and hyperchaotic behaviors are derived theoretically.
Then, the solutions of equilibria are obtained.
For each equilibrium, its stability and existence of Hopf bifurcation are validated.
Based on corresponding first Lyapunov coefficient of each equilibrium, the analytical proof of the existence of periodic solutions is given.
The ultimate bound and positively invariant set for the financial system are obtained and estimated.
There exists a stable periodic solution obtained near the unstable equilibrium point.
Finally, the dynamic behaviors of the new system are explored from theoretical analysis by using the bifurcation diagrams and phase portraits.
Moreover, the hyperchaotic financial system has been simulated using a specially designed electronic circuit and viewed on an oscilloscope, thereby confirming the results of the numerical integrations and its real contribution to engineering.
American Psychological Association (APA)
Kai, G.& Zhang, Wei& Wei, Zhouchao& Wang, J. F.& Akgul, Akif. 2017. Hopf Bifurcation, Positively Invariant Set, and Physical Realization of a New Four-Dimensional Hyperchaotic Financial System. Mathematical Problems in Engineering،Vol. 2017, no. 2017, pp.1-13.
https://search.emarefa.net/detail/BIM-1189849
Modern Language Association (MLA)
Kai, G.…[et al.]. Hopf Bifurcation, Positively Invariant Set, and Physical Realization of a New Four-Dimensional Hyperchaotic Financial System. Mathematical Problems in Engineering No. 2017 (2017), pp.1-13.
https://search.emarefa.net/detail/BIM-1189849
American Medical Association (AMA)
Kai, G.& Zhang, Wei& Wei, Zhouchao& Wang, J. F.& Akgul, Akif. Hopf Bifurcation, Positively Invariant Set, and Physical Realization of a New Four-Dimensional Hyperchaotic Financial System. Mathematical Problems in Engineering. 2017. Vol. 2017, no. 2017, pp.1-13.
https://search.emarefa.net/detail/BIM-1189849
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1189849