The central problem of fully developed turbulence is understanding the energy cascading process and multiscale interaction. Update, there is no deductive theory which leads to a full physical understanding or mathematical formulation. The definition, development,challenge and the corresponding status of turbulence cascade were briefly reviewed. The limitation of present methods were emphasized. Based on the Karman-Howarth equation in 3D incompressible fluid, a new isotropic turbulence scale evolution equation and its related theory progress, the existence of nonlinear dynamic system measured by turbulence Taylor microscale was proven. The present results indicate that the energy cascading process has remarkable similarities with the determinisitic construction rules of the logistic map. The cascade appears as an infinite sequence of period-doubling vortex bifurcations.