Study on Lyapunov Characteristic Exponents of a nonlinear differential equation system

Some basic problems of Lyapunov Characteristic Exponents (LCE) are discussed, including the computational method and the fact that the Lyapunov exponent of any limit set other than an equilibrium point must be zero, namely one 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 yielded. An efficient method for calculating the conditional LCEs is suggested. By studying the conditional LCEs of the hyper-chaotic system, we conclude that it cannot be synchronized with only one driving variable. The infection of random initial values in Wolf's program of LCEs computation is pointed out.