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The existence of codimension-two bifurcation in a discrete SIS epidemic model with standard incidence. (English) Zbl 1269.92062
Summary: We investigate the dynamical complexity of a discrete SIS epidemic model with standard incidence by qualitative analysis and numerical simulations. It is verified that there are codimension-two bifurcations associated with 1:2 and 1:4 strong resonances and chaos phenomena. The results are established by using 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-dimensional space. The results obtained show that a discrete SIS epidemic model can have very rich dynamical behaviors.

MSC:
92D30 Epidemiology
37N25 Dynamical systems in biology
39A28 Bifurcation theory for difference equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
92-08 Computational methods for problems pertaining to biology
39A60 Applications of difference equations
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