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Guckenheimer, J. and Holmes, P. (1983) Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields. Springer, New York.
https://doi.org/10.1007/978-1-4612-1140-2

has been cited by the following article:

• TITLE: The Dynamic Behavior of a Discrete Vertical and Horizontal Transmitted Disease Model under Constant Vaccination

  AUTHORS: Mingshan Li, Xiumin Liu, Xiaoliang Zhou

  KEYWORDS: Vertical and Horizontal Transmission, Vaccination, Center Manifold, Transcritical Bifurcation, Flip Bifurcation

  JOURNAL NAME: International Journal of Modern Nonlinear Theory and Application, Vol.5 No.4, November 18, 2016

  ABSTRACT: In this paper, a class of discrete vertical and horizontal transmitted disease model under constant vaccination is researched. Under the hypothesis of population being constant size, the model is transformed into a planar map and its equilibrium points and the corresponding eigenvalues are solved out. By discussing the influence of coefficient parameters on the eigenvalues, the hyperbolicity of equilibrium points is determined. By getting the equations of flows on center manifold, the direction and stability of the transcritical bifurcation and flip bifurcation are discussed.