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

A one-dimensional iterative chaotic map with infinite collapses within symm etrical region [-1,0) boolean OR (0, +1] is proposed. The stability of fixe d points and that around the singular point are analyzed. Higher Lyapunov e xponents of proposed map show stronger chaotic; characteristics than some i terative and continuous chaotic models usually used. There exist inverse bi furcation phenomena and special main periodic windows at certain positions shown in the bifurcation diagram, which: can explain the generation mechani sm of chaos. The chaotic model with good properties can be generated if cho osing the parameter of the map properly. Stronger inner pseudorandom charac teristics can also be observed through chi (2) test On the supposition of e ven distribution. This chaotic model may have many advantages in practical use.