Analysis of codimension 2 bifurcations for high-dimensional discrete systems using symbolic computation methods

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.