Stability and bifurcation analysis on adiscrete-time system of two neurons

AbstractWe consider a discrete-time system modelling a network of two neurons. The situationwith self-connections is addressed in terms of stability and bifurcation analysis. Choosing an appropriate bifurcation parameter, we prove that the Neimark-Sacker bifurcation occurs when the bifurcation parameter exceeds a critical value. The direction and stability of bifurcation are determined by the normal form theory and center manifold theorem. Results of some computer simulations are displayed graphically