In this paper we consider the abundance of nonhyperbolic strange attractors for families of multi-modal maps and prove that there exists a positive measure set in the multi-dimensional parameter space such that the corresponding systems admit absolutely continuous invariant measures.

Dynamics of the attractor of nonhyperbolic two-dimensional maps was analysed using multifractal theory, and found that the neighborhood of homoclinic tangerncy points of nonhyperbolic attractor exist first order phase transition.

Three methods are used to judge the signal maintaining chaos characteristics or not: watching the strange attractor in three-dimensional phase space,computing the largest Lyapunov exponent by the equation it meets and wolf method,and computing self-power spectrum densit.

A turbulent fluid is a complex nonlinear large system and it is impossible as well as unnecessary to make detailed study of the geometrical structure and dynamical behavior of its strange attractors.

This text expounds its influence on preschool curriculum objectives, content designing, implementation and evaluation with brief introduction of butterfly effect, self-similarity structure, strange attractor, non-linear phenomenon, which appear as the basic features of theory of Chaos.

By simu-lating with computer, the strange attractors, and self-likel.