Chaotic characteristics of a one-dimensional iterative map with infinite collapses

A one-dimensional iterative chaotic map with infinite collapses within symmetrical region [-1, O)/spl cup/(O, +1] is proposed. The stability of fixed points and that around the singular point are analyzed. Higher Lyapunov exponents of proposed map show stronger chaotic characteristics than some iterative and continuous chaotic models usually used. There exist inverse bifurcation phenomena and special main periodic windows at certain positions shown in the bifurcation diagram, which can explain the generation mechanism of chaos. The chaotic model with good properties can be generated if choosing the parameter of the map properly. Stronger inner pseudorandom characteristics can also be observed through /spl chi//sup 2/ test on the supposition of even distribution. This chaotic model may have many advantages in practical use.