Stability Analysis and Hopf Bifurcation Control for a Wireless Network Model

A wireless network model with the hybrid control is considered. The stability and Hopf bifurcation behavior of the wireless network model are investigated. The stability analysis and the parameter condition that the Hopf bifurcation occurs are deduced. The stability and direction of the bifurcating periodic solutions are analyzed by applying the normal form theory and the center manifold theorem. Numerical simulations demonstrate the complex behavior of the system and verify the theoretical analysis.