Solutions of dynamical systems described by nonlinear differential equations frequently change their behavior as the parameter varies, e.g., the period is doubled, the solution is disappeared, or sometimes chaotic motion is generated. Such change of stability for the solution is called bifurcation, and it is important to obtain the bifurcation parameter values to understand concrete properties of the dynamical system. We develop two surface visualization methods for showing bifurcation structures in the 3D parameter space. One of them constructs surfaces accurately from 2nd dimensional bifurcation diagrams. The other can calculate sufficient amount of vertex information to construct a surface itself. From these 3D bifurcation surfaces, global properties of the system can be clarified, and especially it is possible to estimate the parameter range where the system behaves chaotically.

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Stripe structure in turbulent boundary layer has been clearly visualized by a combination of a shear stress imaging chip using MEMS (Micro-Electro-Mechanical-Systems) and discrete wavelets transform. In details, the structure in lower Reynolds number is shown clearly on the lower frequency wavelets level, the structure in high Reynolds number is done clearly on the higher frequency wavelets level. The MEMS shear stress sensor is designed and fabricated by surface micromachining technology, contributing to obtaining the time-space two dimensional shear stress data. The discrete wavelets transform is a software technique to decompose the frequency level with the time and space information of the wave. The experiments for shear stress distribution were carried out on Re = 6960, 12180 and 17400.

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