Dynamical analysis of the hyperchaos Lorenz system
Abstract
This article deals with the ultimate bound on the trajectories of the hyperchaos Lorenz system based on Lyapunov stability theory. The innovation of this article lies in that the method of constructing Lyapunov functions applied to the former chaotic systems is not applicable to this hyperchaos system, and moreover, one Lyapunov function can not estimate the bounds of this hyperchaos Lorenz system. We successfully estimate the bounds of this hyperchaos system by constructing three generalized Lyapunov functions step by step. Some computer simulations are also given to show the effectiveness of the proposed scheme. © 2016 Wiley Periodicals, Inc. Complexity 21: 440–445, 2016
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The hyperchaotic Lorenz system with parameters b=8/3, a=10, c=28, and r=1 behaves in a hyper-chaotic manner.
“When b = 8/3, a = 10, c = 28, and r = 1, the system behaves in a hyper-chaotic manner.”
From A Bijective Image Encryption System Based on Hybrid Chaotic Map Diffusion and DNA Confusion (2020) · cites this paper as [37]
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A Bijective Image Encryption System Based on Hybrid Chaotic Map Diffusion and DNA Confusion
ElKamchouchi, D. H., Mohamed, H. G., & Moussa, K. H. (2020) · Entropy · doi:10.3390/e22020180 · Cited by 63 · see citing works
“In addition, they [36,37] have reported the hyper‐ chaos Lorenz system as”
Background
- Authors
- Zhang, F., & Zhang, G.
- Affiliations
- Chongqing Technology and Business University (CN)
- Corresponding author
- Zhang, Fuchen
- Venue
- Complexity
- Publisher
- Wiley
- Published
- 2016-02-09
- Volume
- 21
- Issue
- S1
- Pages
- 440-445
- ISSN
- 1076-2787 (ISSN-L)
- OpenAlex
- W2339543578
- Cited by
- 6
- References
- 0
- Citations by year
- 2024: 1 · 2023: 1 · 2022: 1 · 2020: 1 · 2018: 1 · 2017: 1
- FWCI
- 0.38
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- Locations
- Complexity (publishedVersion)
- Funders
- National Natural Science Foundation of China (11426047, 11501064)
- Basic and Advanced Research Project of CQCSTC (cstc2014jcyjA00040)
- Scientific and Technological Research Program of Chongqing Municipal Education Commission (KJ1500605)
- Research Fund of Chongqing Technology and Business University (2014-56-11)
- Topics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Chaos control and synchronization
- Physical Sciences › Mathematics › Mathematical Physics › Mathematical Dynamics and Fractals
- Physical Sciences › Mathematics › Geometry and Topology › Advanced Differential Equations and Dynamical Systems
- Keywords
- hyperchaos, Lorenz system, ultimate bound, Lyapunov function, generalized Lyapunov function, chaotic systems, trajectory bounds
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