On Symbolic Computation of the LCE of N-Dimensional Dynamical Systems
Abstract
In the present paper, based on our earlier work, we propose a systematic method for symbolically computing the Lyapunov characteristic exponents, briefly LCE, of n-dimensional dynamical systems. First, we analyze in mathematics the LCE of n-dimensional dynamical systems. In particular, as an example, we discuss the LCE of the Lorenz systems. Then, to do the above task, a framework on representation and manipulation of a class of non-algebraic objects using non-standard analysis (NSA) is established. In this framework, an algorithm can be developed for deriving some unknown relations on some objects involving limit processes. Finally, applying this algorithm to n-dimensional dynamical systems, we can show that their maximal LCE can be derived mechanically; particularly, for the Lorenz systems, we obtain an important result on the maximal LCE of the chaotic attractors of these systems — their dependence on the systems parameters.
Keywords
Dynamical system LCE symbolic computation non-algebraic objectPreview
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