Example of robust chaos in a smooth map
Department of Physics, University of Lethbridge -
4401 University Drive
Lethbridge, AB, T1K 3M4, Canada
Accepted: 22 February 2001
Robust chaos is defined by the absence of periodic windows and coexisting attractors in some neighborhood of the parameter space. The occurrence of robust chaos has been discussed in Phys. Rev. Lett., 78 (1997) 4561 and Phys. Rev. Lett., 80 (1998) 3049. It has been shown that robust chaos can occur in piecewise smooth systems. Also, it has been conjectured that robust chaos cannot occur in smooth systems. However, here we give a counterexample to this conjecture. We present a one-dimensional smooth map that generates robust chaos in a large domain of the parameter space .
PACS: 05.45.-a – Nonlinear dynamics and nonlinear dynamical systems
© EDP Sciences, 2001