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Numerical computation for high dimension Hopf bifurcation. (Chinese. English summary) Zbl 0786.65048

The authors consider a nonlinear dynamical system with a parameter \(\lambda: \dot x = F(x,\lambda)\), where \(F: X\times \Lambda \to \mathbb{R}^ n\), and \(X\subset\mathbb{R}^ n\) and \(\Lambda\subset \mathbb{R}\). Using a simple matrix transform, the problem of finding the Hopf bifurcation points of the nonlinear dynamical system changes to the one of computing a pair of complex conjugate eigenvalues with maximum norm of the transformed matrix of the Fréchet derivative matrix. Finally, they present numerical computational examples to show the effectiveness of their algorithm.

MSC:

65H17 Numerical solution of nonlinear eigenvalue and eigenvector problems
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