Abstract
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.
