The whole process of the change of Willamowski?R?ssler chemistry system from period motions to chaotic motions through double?period bifurcation, as well as the change from chaotic motions to period motions. We present bifurcation diagram, Lyapunov exponent spectrum, Poincare section, power spectrum and return map of the system, and the chaotic behavior of the model is also revealed. The adaptive and nonlinear controllers are designed, and the theoretical analysis and numerical simulation show that the chaos of the non?dimensional form of Willamowski?R?ssler system can be controlled effectively. Drive?Response method is used to realize the global exponential synchronization. The simulation results show that the Drive?Response method is effective.