Geodesic
A Neimark-Sacker bifurcation in a discrete SIS model
Mathematica Applicanda, Tome 51 (2023) no. 1, pp. 109-120.

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In this paper, we analyze a possibility of occurrence of a Neimark-Sacker bifurcation in a two-dimensional SIS discrete-time model. As a discretization method, we applied the Explicit Euler Scheme. We choose a step size of discretization method as a bifurcation parameter, what is not a typical approach. We phrase conditions giving the bifurcation appearance depending on the step size. Firstly, we determine terms on the step size enabling the eigenvalues of Jacobian matrix for the endemic stationary state of the system being complex and having absolute value equal to 1. Then we use the Center Manifold Theorem in order to exclude values of step size which disable the occurrence of bifurcation. We accomplish our results with numerical simulations.
DOI : 10.14708/ma.v51i1.7203
Classification : 92B05, 39A28
Mots-clés : Neimark-Sacker bifurcation, discretization, Explicit Euler Method, discrete dynamical system, epidemiology 
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Marcin Choiński. A Neimark-Sacker bifurcation in a discrete SIS model. Mathematica Applicanda, Tome 51 (2023) no. 1, pp.  109-120. doi : 10.14708/ma.v51i1.7203. http://geodesic.mathdoc.fr/articles/10.14708/ma.v51i1.7203/

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