Oscillation deduced from the Neimark-Sacker bifurcation in a discrete dual Internet congestion control algorithm

摘要

In this paper, we consider a dual Internet congestion control algorithm applied to a nonstandard finite-difference scheme, which responds to congestion signals from the network. By choosing delay as a bifurcation parameter, the local asymptotic stability of the positive equilibrium and the existence of Neimark-Sacker bifurcations are analyzed. Then the explicit algorithm for determining the direction of Neimark-Sacker bifurcations and the stability of invariant closed curves are derived. In addition, we give specific examples to illustrate the phenomenon that coincides with our theoretical results. MSC:34K18, 34K20.