Study on Lyapunov characteristic exponents of a nonlinear differential equation system

Some basic problems of Lyapunov Characteristic Exponents (LCE) are discusse d, including the computational method and the fact that the Lyapunov expone nt of any limit set other than an equilibrium point must be zero, namely on e of the Lyapunov exponents should vanishes. The conclusion is deduced that the dimension of a hyper-chaotic attractor must be great than 3. The LCEs of several important models are studied, more reasonable results are yielde d. An efficient method for calculating the conditional LCEs is suggested. B y studying the conditional LCEs of the hyper-chaotic system, we conclude th at it cannot be synchronized with only one driving variable. The infection of random initial values in Wolf's program of LCEs computation is pointed o ut.