This thesis consists of four parts: (1) the chaotic behaviors of Double-Froude system are studied numerically by phase portraits, Pooincaré maps, bifurcation diagrams and Lyapunov exponent diagrams. (2) generalized synchronization and control of chaos is studied by GYC partial region stability theory. (3) the Rössler system with Legendre function is studied for chaos, hyperchaos and synchronization. (4) Yin-Yang generalized synchronization (YYGS) of Yang Lü and Yin Lü systems are studied by adaptive control based on pragmatical asymptotical stability theory.