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Symbolic computation of limit cycles associated with Hilbert’s 16th problem. (English) Zbl 1221.34082

Summary: This paper is concerned with the practical complexity of the symbolic computation of limit cycles associated with Hilbert’s 16th problem. In particular, in determining the number of small-amplitude limit cycles of a non-linear dynamical system, one often faces computing the focus values of Hopf-type critical points and solving lengthy coupled polynomial equations. These computations must be carried out through symbolic computation with the aid of a computer algebra system such as Maple or Mathematica, and thus usually gives rise to very large algebraic expressions. In this paper, efficient computations for the focus values and polynomial equations are discussed, showing how to deal with the complexity in the computation of non-linear dynamical systems.

MSC:

34C07 Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert’s 16th problem and ramifications) for ordinary differential equations
34-04 Software, source code, etc. for problems pertaining to ordinary differential equations
68W30 Symbolic computation and algebraic computation

Software:

Mathematica; Maple
PDFBibTeX XMLCite
Full Text: DOI

References:

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