离散的扩充BVP振子的分支研究

Nishiuchi在经典的BVP振子的基础上提出了扩充BVP振子,并通过数值模拟分析了系统的复杂动态.有关文献已经讨论了连续的扩充BVP振子的复杂性.作者致力于离散的扩充BVP振子的研究,利用稳定性理论和分支理论,首先分析出系统存在两类不动点,并分别讨论其稳定性条件,其次,对原点不动点随参数变化产生的分支进行了详细的讨论,得出系统局部发生Hopf分支、Pitchfork分支的条件.随之,对非原点不动点的Hopf分支曲面进行了分析,最后,通过对振子进行数值模拟,验证了理论结果.

Bifurcations of a Discrete Extended BVP Oscillator

Nishiuchi gives a three-dimension system named extended B VP equation, furthermore, ne analyzed sophisticated dynamical phenomena with simulations. Some documents have talked about consisted extended BVP oscillator. The authors are committed to discrete extended equations. With taking advantage of theory of fixed point and bifurcations, the authors firstly put forward that there are two kinds of fixed points and analyze their stability conditions. Next, the authors give existing conditions for bifurcations of Hopf and Pitchfork,based on detailed analysis of the parameters＇ diversifications. What＇s more, conditions for Hopf bifurcation at non origin fixed points are provided. Finally, the authors test and verify previous conclusions with numerical simulation.