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Analysis of codimension 2 bifurcations for high-dimensional discrete systems using symbolic computation methods. (English) Zbl 1410.39012

Summary: This article reports an algebraic criterion of the eigenvalue assignment, transversality condition and non-resonance condition for fold-N-S bifurcations. By means of symbolic computation methods, we propose an algorithmic approach for systematically analyzing codimension 2 bifurcations for high-dimensional discrete systems. The effectiveness of the proposed symbolic approach is verified by experiments. In particular, the flip- and fold-N-S bifurcations of a five-dimensional discrete dynamical system with a washout-filter feedback controller are analyzed.

MSC:

39A12 Discrete version of topics in analysis
37M20 Computational methods for bifurcation problems in dynamical systems

Software:

SYNRAC; DISCOVERER
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