ROBUST CHAOS IN A SMOOTH SYSTEM

Abstract

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 [Phys. Rev. Lett.78, 4561 (1997); ibid.80, 3049 (1998)]. 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 counter example to this conjecture. We present a one-dimensional smooth map xt + 1 = f(xt, α) that generates robust chaos in a large domain of the parameter space (α). An application to random number generation and cryptography is also presented.