A chaotic system with only one stable equilibrium
By Xiong Wang, Guanrong Chen. 2011
424 citations recorded by the source corpus.
Abstract If you are given a simple three-dimensional autonomous quadratic system that has only one stable equilibrium, what would you predict its dynamics to be, stable or periodic? Will it be surprising if you are shown that such a system is actually chaotic? Although chaos theory for three-dimensional autonomous systems has been intensively and extensively studied since the time of Lorenz in the 1960s, and the theory has become quite mature today, it seems that no one would anticipate a possibility of finding a three-dimensional autonomous quadratic chaotic system with only one stable equilibrium. The discovery of the new system, to be reported in this Letter, is indeed striking because for a three-dimensional autonomous quadratic system with a single stable node-focus equilibrium, one typically would anticipate non-chaotic and even asymptotically converging behaviors. Although the equilibrium is changed from an unstable saddle-focus to a stable node-focus, therefore the familiar Si’lnikov homoclinic criterion is not applicable, it is demonstrated to be chaotic in the sense of having a positive largest Lyapunov exponent, a fractional dimension, a continuous broad frequency spectrum, and a period-doubling route to chaos.
Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/dac522289ce09879de72510709d1aa81429870b8
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In Computer Networks and Communications
In Statistical and Nonlinear Physics
Citations in the corpus
- Hidden attractors in dynamical systems (2016, neutral): “[107] M.-F. Danca, M. Feckan, N. Kuznetsov, G. Chen, Looking more closely to the Rabinovich-Fabrikant system, Int.”
- Simple chaotic flows with a line equilibrium (2013, background): “That is the reason such systems are rarely found, and only a few such examples have been reported in the literature [11–20].”
- Simple Chaotic flows with One Stable equilibrium (2013, background): “Only a few such examples have been reported in the literature [Jafari et al., 2013; Wei, 2011a, 2011b; November 29, 2013 12:56 WSPC/S0218-1274 1350188 M. Molaie et al. Wang & Chen, 2012, 2013; Wei & Yang, 2010, 2011, 2012; Wang et al., 2012a, 2012b].”