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Hidden Hyperchaotic Attractors in a Modified Lorenz–Stenflo System with Only One Stable Equilibrium
Abstract
This paper reports the finding of a four-dimensional (4D) non-Sil'nikov autonomous system with three quadratic nonlinearities, which exhibits some behavior previously unobserved: hidden hyperchaotic attractors with only one stable equilibrium. The algebraical form of the non-Sil'nikov chaotic attractor is very similar to the hyperchaotic Lorenz–Stenflo system but they are different and, in fact, nonequivalent in topological structures. Of particular interest is the fact this system has only one stable equilibrium, but can exhibit hidden hyperchaos, chaos, periodic orbit. Moreover, the coexistence of attracting sets can be obtained in the system for some parameter values and different initial conditions, such as hyperchaotic attractor and point, hyperchaotic attractor and period orbit. To further analyze the new system, the ultimate bound and positively invariant set for the modified hyperchaotic Lorenz–Stenflo system are also obtained. Moreover, the complete mathematical characterizations for 4D Hopf bifurcation are rigorously derived and studied.
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Cites
Determining Lyapunov exponents from a time series
Wolf, A., Swift, J. B., Swinney, H. L., & Vastano, J. A. (1985) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(85)90011-9 · Cited by 9,499
CHEN, G., & UETA, T. (1999) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127499001024 · Cited by 2,838
Cited by
Hidden attractors in dynamical systems
Dudkowski, D., Jafari, S., Kapitaniak, T., Kuznetsov, N. V., Leonov, G. A., & Prasad, A. (2016) · Physics Reports · doi:10.1016/j.physrep.2016.05.002 · Cited by 695
Leonov, G. A., Kuznetsov, N. V., & Mokaev, T. N. (2015) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2015-02470-3 · Cited by 386
The design and implementation of hybrid RSA algorithm using a novel chaos based RNG
Çavuşoğlu, Ü., Akgül, A., Zengin, A., & Pehlivan, I. (2017) · Chaos, Solitons & Fractals · doi:10.1016/j.chaos.2017.09.025 · Cited by 41
Metadata
- Authors
- Wei, Z., & Zhang, W.
- Venue
- International Journal of Bifurcation and Chaos
- Publisher
- World Scientific Pub Co Pte Lt
- Published
- 2014-10
- Volume
- 24
- Issue
- 10
- Pages
- 1450127
- ISSN
- 0218-1274 (ISSN-L)
- 1793-6551
- OpenAlex
- W2111360810
- Cited by
- 159
- References
- 2
- FWCI
- 10.55
- Type
- journal article
- Language
- en
- Open access
- closed
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- Wei, Z., & Zhang, W. (2014). Hidden Hyperchaotic Attractors in a Modified Lorenz–Stenflo System with Only One Stable Equilibrium. International Journal of Bifurcation and Chaos. https://doi.org/10.1142/s0218127414501272
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