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The existence of codimension-two bifurcation in a discrete SIS epidemic model with standard incidence

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Abstract

In this paper, we investigate the dynamical complexity of a discrete SIS epidemic model with standard incidence by the qualitative analysis and numerical simulations. It is verified that there are the codimension-two bifurcations associated with 1:2 and 1:4 strong resonances and chaos phenomena. The results are established by using the bifurcation theory and the normal form method. Furthermore, the numerical simulations are obtained by the phase portraits, the codimension-two bifurcation diagrams, and the maximum Lyapunov exponents diagrams for two different varying parameters in a 3-dimension space. The results obtained in this paper show that a discrete SIS epidemic model can have very rich dynamical behaviors.

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Acknowledgements

The authors are very grateful to the editor and anonymous referees for their valuable comments and helpful suggestions, which led to a great improvement of the original manuscript. This work was supported by the National Natural Science Foundation of P.R. China (Grant Nos. 10961022, 10901130) and the Natural Science Foundation of Xinjiang (Grant No. 2010211A07).

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Correspondence to Zhidong Teng.

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Chen, Q., Teng, Z., Wang, L. et al. The existence of codimension-two bifurcation in a discrete SIS epidemic model with standard incidence. Nonlinear Dyn 71, 55–73 (2013). https://doi.org/10.1007/s11071-012-0641-6

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