ROBUST CHAOS IN A SMOOTH SYSTEM

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  • M. ANDRECUT
    Department of Physics, University of Lethbridge, 4401 University Drive, Lethbridge, AB, T1K 3M4, Canada
  • M. K. ALI
    Department of Physics, University of Lethbridge, 4401 University Drive, Lethbridge, AB, T1K 3M4, Canada

Abstract

<jats:p> 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 x<jats:sub>t + 1</jats:sub> = f(x<jats:sub>t</jats:sub>, 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. </jats:p>

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