This paper examines the asymptotic behavior of solutions of a simple network model using feedback control under the presence of delays. It shows numerically the existence of complex asymptotic behavior dependent on both parameter values and initial conditions. The presence of multiple asymptotic periodic orbits of different characteristics at the same parameter values indicates that the interaction of asymptotic behavior with parameter ranges and initial histories is an extremely delicate matter.
Giampiero Pecelli, B. G. Kim