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Constructing a chaotic system with any number of equilibria
Open accessAbstract
In the chaotic Lorenz system, Chen system and Rössler system, their equilibria are unstable and the number of the equilibria are no more than three. This paper shows how to construct some simple chaotic systems that can have any preassigned number of equilibria. First, a chaotic system with no equilibrium is presented and discussed. Then a methodology is presented by adding symmetry to a new chaotic system with only one stable equilibrium, to show that chaotic systems with any preassigned number of equilibria can be generated. By adjusting the only parameter in these systems, one can further control the stability of their equilibria. This result reveals an intrinsic relationship of the global dynamical behaviors with the number and stability of the equilibria of a chaotic system.
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CHEN, G., & UETA, T. (1999) · International Journal of Bifurcation and Chaos · doi:10.1142/s0218127499001024 · Cited by 2,838
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Elementary quadratic chaotic flows with no equilibria
Jafari, S., Sprott, J. C., & Hashemi Golpayegani, S. M. R. (2013) · Physics Letters A · doi:10.1016/j.physleta.2013.01.009 · Cited by 493
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
S-Box Based Image Encryption Application Using a Chaotic System without Equilibrium
Wang, X., Çavuşoğlu, Ü., Kacar, S., Akgul, A., Pham, V.-T., Jafari, S., Alsaadi, F. E., & Nguyen, X. Q. (2019) · Applied Sciences · doi:10.3390/app9040781 · Cited by 125
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Metadata
- Authors
- Wang, X., & Chen, G.
- Venue
- Nonlinear Dynamics
- Published
- 2012-11-08
- Volume
- 71
- Issue
- 3
- Pages
- 429-436
- ISSN
- 0924-090X (ISSN-L)
- 1573-269X
- OpenAlex
- W2964079314
- Cited by
- 270
- References
- 1
- FWCI
- 12.89
- Type
- journal article
- Language
- en
- Open access
- green
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