中立型反馈控制差分模型的分支分析及仿真

摘要

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 bifurca-tion 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 bifurca-tion. Numerical examples are carried out to illustrate the correctness and realizability of theoretical results.%讨论了具有时滞的中立型反馈控制Logistic差分模型的稳定性及Flip分支；运用特征值理论和Jury判据得到正平衡态局部渐近稳定的充分条件；选取系统中的某一个参数为分支参数，利用分支理论和中心流形定理给出并分析了Flip分支的存在性条件、规范型、稳定性及方向；通过实例和计算机仿真验证了定理条件的可实现性与结论的正确性。