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A numerical algorithm for computing Neimark-Sacker bifurcation parameters

We propose an efficient method for computing parameter values of the Neimark-Sacker bifurcation in this paper. To handle the complex eigenvalue problem, we expand the characteristic equation into a sum of determinants of the involving matrices. We solve for the location of the fixed point, period, parameter, and arguments of the complex eigenvalues for the bifurcation simultaneously, by using Newton's method and solutions of variational equations. This algorithm does not rely on the analytic structure of the underlying system.