Hopf bifurcation for a small-world network model with parameters delay feedback control

To delay the onset of undesirable bifurcation, the bifurcation control has become a subject of intense research activities. In this paper, a small-world network model with the delay feedback is considered, in which the strength of feedback control is a nonlinear function of delay. With this controller, one can change the critical value of bifurcation, and thus enlarge the stable region. Moreover, by adding some proper slowly varying parts into the bifurcation parameters, the stability can be improved. Numerical results show that the dynamics of the small-world network model with the controller of delay-dependent parameters is quite different from that of a system with the controller of delay-independent parameters only.