Abstract
We consider the discretizations of parameter-dependent, continuous-time dynamical systems. We show that the general one-step methods shift a generalized Hopf bifurcation and turn it into a generalized Neimark–Sacker point. We analyze the effect of discretization methods on the emanating Hopf curve. In particular, we obtain estimates for the eigenvalues of the discretized system along this curve. A detailed analysis of the discretized first Lyapunov coefficient is also given. The results are illustrated by a numerical example. Dynamical consequences are discussed.
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J. Páez Chávez was supported by CRC 701 ‘Spectral Structures and Topological Methods in Mathematics’, Bielefeld University.
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Páez Chávez, J. Discretizing dynamical systems with generalized Hopf bifurcations. Numer. Math. 118, 229–246 (2011). https://doi.org/10.1007/s00211-010-0340-5
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DOI: https://doi.org/10.1007/s00211-010-0340-5