关键词: 中立型, 时滞, 反馈控制, 稳定性, Flip分支

Abstract: The stability and bifurcation behaviors of feedback control difference system with time delay are investigated. The sufficient conditions for the local asymptotic stability of the positive equilibrium are achieved based on the theory of characteristic value and Jury criterion. It chooses a parameter of the system as the bifurcation parameter and uses bifurcation theory and the center manifold theorem, it gets that the difference model undergoes a flip bifurcation at an exceptive value of the bifurcation parameter, and more it analyzes the existence conditions, normal form and direction of the bifurcation. Numerical examples are carried out to illustrate the correctness and realizability of theoretical results.

Key words: neutral type, delay, feedback control, stability, Flip bifurcation