Stability and bifurcation analysis in the cross-coupled laser model with delay

The dynamics of the cross-coupled laser model with delay has been investigated. The investigation confirms that a Hopf bifurcation occurs due to the existence of stability switches when the product of the coupling strengths varies. An algorithm for determining the stability and direction of the Hopf bifurcation is derived by applying the normal form theory and the center manifold theorem. Finally, some numerical simulations are carried out to illustrate the analytic results.