Stability Changes of Periodic Solutions to a Coupled Nonlinear Equation with Time Delay

We shall consider a linear difference coupled equation with time delay and discuss a Hopf bifurcation of this equation. In the case of weakly coupling, it will be shown that two types of periodic solutions bifurcate from the steady state for some parameter values, and that those periodic solutions exchange the stability under certain conditions; moreover, under another conditions one of tho..