Recently there has been increasing interest in finding and studying rare examples of simple chaotic systems such as those in which there are no equilibria or in which any existing equilibria are stable [1-7]. They belong to a new defined category of chaotic systems which is called “chaotic systems with hidden attractor” [8-9]. However they are all about chaotic flows and I haven’t seen any similar work about chaotic maps. Does anybody know about a chaotic map with no equilibria or only stable equilibria?
References
[1] Jafari, S., Sprott, J.C., Golpayegani, S.M.R.H. [2013] “Elementary quadratic chaotic flows with no equilibria,” Phys. Lett. A, 377, 699-702.
[2] Wei, Z. [2011] “Dynamical behaviors of a chaotic system with no equilibria,” Phys. Lett. A 376, 102-108.
[3] Wang, X., Chen, G. [2012] “A chaotic system with only one stable equilibrium,” Commun.Nonlinear Sci. Numer.Simulat. 17, 1264-1272.
[4] Wang, X., Chen, G. [2013] “Constructing a chaotic system with any number of equilibria,” Nonlinear Dyn. 71, 429-436.
[5] Wei, Z., Yang, Q. [2012] “Dynamical analysis of the generalized Sprott C system with only two stable equilibria,” Nonlinear Dyn. 68, 543-554.
[6] Malihe Molaie, Sajad Jafari, J. C. Sprott, S. Mohammad Reza Hashemi Golpayegani, “Simple chaotic flows with one stable equilibrium,” International Journal of Bifurcation and Chaos, In press.
[7] Sajad Jafari, J. C. Sprott, “Simple chaotic flows with a line equilibrium,” Chaos Solitons Fract, In press.
[8] Leonov, G.A., Kuznetsov, N.V., Vagaitsev, V. I., [2011] “Localization of hidden Chua’s attractors,” Phys. Lett. A 375, 2230–2233.
[9] Leonov, G.A., Kuznetsov, N.V. Vagaitsev, V.I., [2012] “Hidden attractor in smooth Chua systems,” Physica D 241, 1482–1486.