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A new map for chaotic communication

We propose in this paper a new one-dimensional chaotic map based on the hyperbolic tangent function that depends on a single control parameter r. The Lyapunov exponent of this map remains practically unaltered with the variation of r. Two new statistics are proposed to study the chaotic dynamic characteristics of chaotic maps, namely, the spread rate, and the contraction factor. The proposed map may be employed in chaotic communication systems based on symbolic dynamics with advantages over current approaches that uses piecewise linear maps.