Typical nonlinear dynamical chaotic images and their improvements

When using chaotic variables to solve optimization problems and encryption problems, it needs to study different dimension of chaotic images. We studied nonlinear dynamics systems performance about several chaotic images in different dimensions, including the phase diagram, Lyapunov exponent, probability density, etc. In order to improve their chaotic performance, the improvement measures were given for one-dimension tent system and two-dimension henon system, and a new chaotic system were proposed, it was two-dimension logistic system. It contained nolinear factor, the new system possessed higher level of complexity. Therefore, we can overcome the chaotic crisis of tent image, improve the probability density of henon system and obtain new higher-quality chaotic system 2d-logistic from the existence chaotic systems. The Runge-Kutta method for hyperchaos system was given, and applied it to the three-dimensional Lorenz chaotic system, we acquired its diagram in different axis efficiently. The simulation experiments were conducted, and the comparison test results were analyzed in detail. The study provides important scientific support to the improvement and application of chaotic systems.