Constructing a chaotic system with any number of equilibria

By Xiong Wang, Guanrong Chen. 2012

277 citations recorded by the source corpus.

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.

Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/10b67a2c3ce845e942d1ed1f7dff816183e635b3

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In Computer Networks and Communications

In Statistical and Nonlinear Physics

Citations in the corpus

A Memristor-Based Hyperchaotic System with Hidden Attractors: Dynamics, Synchronization and Circuital Emulating (2015, background): “Studying systems with hidden attractors is a new research direction because of their practical and theoretical importance [48-53].”
Elementary quadratic chaotic flows with no equilibria (2013, methodology): “Recently, two other dissipative examples have been reported, which we call the Wei system [1] listed as NE2 in Table 1 and the Wang– Chen system [2], a simplified version of which with one fewer term than previously published is listed as NE3 in Table 1.”
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].”
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].”
Hidden attractors in dynamical systems (2016, background): “and Chen in [73], Jafari and Sprott in [83] have introduced simple chaotic systems with a line of equilibria.”