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Coexisting Hidden Attractors in a 4-D Simplified Lorenz System
Abstract
A new simple four-dimensional equilibrium-free autonomous ODE system is described. The system has seven terms, two quadratic nonlinearities, and only two parameters. Its Jacobian matrix everywhere has rank less than 4. It is hyperchaotic in some regions of parameter space, while in other regions it has an attracting torus that coexists with either a symmetric pair of strange attractors or with a symmetric pair of limit cycles whose basin boundaries have an intricate fractal structure. In other regions of parameter space, it has three coexisting limit cycles and Arnold tongues. Since there are no equilibria, all the attractors are hidden. This combination of features has not been previously reported in any other system, especially one as simple as this.
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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
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
Hidden extreme multistability in memristive hyperchaotic system
Bao, B. C., Bao, H., Wang, N., Chen, M., & Xu, Q. (2017) · Chaos, Solitons & Fractals · doi:10.1016/j.chaos.2016.11.016 · Cited by 396
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
Dynamical analysis of a simple autonomous jerk system with multiple attractors
Kengne, J., Njitacke, Z. T., & Fotsin, H. B. (2016) · Nonlinear Dynamics · doi:10.1007/s11071-015-2364-y · Cited by 249
A new simple chaotic system and its application in medical image encryption
Liu, J., Ma, Y., Li, S., Lian, J., & Zhang, X. (2018) · Multimedia Tools and Applications · doi:10.1007/s11042-017-5534-8 · Cited by 109
Metadata
- Authors
- Li, C., & Sprott, J. C.
- Venue
- International Journal of Bifurcation and Chaos
- Publisher
- World Scientific Pub Co Pte Lt
- Published
- 2014-03
- Volume
- 24
- Issue
- 03
- Pages
- 1450034
- ISSN
- 0218-1274 (ISSN-L)
- 1793-6551
- OpenAlex
- W2103748903
- Cited by
- 279
- References
- 1
- FWCI
- 20.00
- Type
- journal article
- Language
- en
- Open access
- closed
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- Li, C., & Sprott, J. C. (2014). Coexisting Hidden Attractors in a 4-D Simplified Lorenz System. International Journal of Bifurcation and Chaos. https://doi.org/10.1142/s0218127414500345
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