# Center manifold theory for discrete dynamical systems

## Abstract

Using the center manifold theory for maps, we derive a theorem for the existence of backward bifurcation at bifurcation points of discrete dynamical systems. This theorem is an analogue of a theorem in [3] for continuous dynamical systems. We discuss applications to discrete dynamical systems in general [2], but more specifically those arising as dicretisations of continuous dynamical systems via the nonstandard finite difference method [1].## References

Anguelov, R., Dumont, Y., Lubuma, J.M.-S., Mureithi, E.; Stability Analysis and Dynamics Preserving Nonstandard Finite Difference Schemes for a Malaria Model. Mathematical Population Studies, 20:2(2013), 101-122.

Barrera, J.H., Cintron-Arias, A., Davidenko, N., Denogean, L.R., Franco-Gonzalez, S.R.; Dynamics of a two-dimensional discrete-time SIS model. MTBI, Cornell University Technical Report (1999).

Castillo-Chavez,C., Song, B.; Dynamical models of tuberculosis and their applications. Math. Biosci. Engin., 1(2004) 361-404.