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The relation between the Lyapunov exponent spectrum of a periodically excited non-autono-mous dynamical system and the Lyapunov exponent spectrum of the corresponding autonomous system is givenand the validity of the relation is verified theoretically and computationally.A direct method for calculatingthe Lyapunov exponent spectrum of non-autonomous dynamical systems is suggested in this paper,whichmakes it more eonvenient to calculate the Lyapunov exponent spectrum of the dynamical system periodicallyexcited.Following the definition of the Lyapunov dimension D_L~(A)of the autonomous system,the definition ofthe Lyapunov dimension D_L of the non-autonomous dynamical system is also given,and the difference be-tween them is the integer 1 namely,D_L~(A)-D_L = 1.For a quasi-periodically excited dynamical system,similar conclusions are formed.
The relation between the Lyapunov exponent spectrum of a periodically excited non-autono-mous dynamical system and the Lyapunov exponent spectrum of the corresponding autonomous system is given and the validity of the relation is verified theoretically and computationally. A direct method for calculating the Lyapunov exponent spectrum of non-autonomous dynamical systems is suggested in this paper, whichmakes it more eonvenient to calculate the Lyapunov exponent spectrum of the dynamical system periodicallyexcited.Following the definition of the Lyapunov dimension D_L ~ (A) of the autonomous system, the definition ofthe Lyapunov dimension D_L of the non-autonomous dynamical system is also given, and the difference be-tween them is the integer 1 assume, D_L ~ (A) -D_L = 1. For a quasi-periodically excited dynamical system, similar are formed.