Lissajous chaotic map

Chaos has been widely applied in the fields including pattern recognition, data compression, and autocontrol. It has been attached great importance to for its special use in secrete communication systems. In this paper, we based on the explicit function, which was said to be a random data generator, and proposed a new kind of map called Lissajous chaotic map. It appears completely different deterministic randomness behavior with the known chaotic maps. An iteration system was given to carry out exactly the explicit function X/sub n/ = P(/spl Phi/Tz/sup n/) , when z is a fraction whose numerator and denominator are prime numbers. We also proposed another kind of map, time-delay Lissajous chaotic map, corresponding to Lissajous chaotic map. It has a kind of more complicated dynamical behavior.