摘要
研究了一类具有离散和分布时滞的Lotka-Volterra模型的稳定性和Hopf分支问题。由特征值理论且以时滞为参数,得到正平衡态局部渐近稳定的充要条件和Hopf分支存在的充分条件。根据中心流形定理以及规范型理论,得到分支值附近分支周期解稳定性。用Matlab绘制出模型数值解的图像,验证了所得结论的正确性;并结合图形讨论了各参数变化对分支周期解的影响。
The stability and Hopf bifurcation about Lotka-Volterra model with discrete and distributed delay are investigated.According to the theory of characteristic equation and regarding the delay as parameter,necessary and sufficient condition for the local asymptotical stability of the steady state and the sufficient condition the existence of Hopf bifurcation are obtained.In term of the center manifold and normal form theory,the direction of Hopf bifurcation and the stability of periodic bifurcation solution are discussed.Finally,several numerical examples are given by Matlab to support the theoretical conclusions,besides the influence of every parameter for the bifurcated periodic solutions are discussed by compare the pictures.
出处
《科学技术与工程》
2011年第15期3366-3371,3376,共7页
Science Technology and Engineering
基金
国家自然科学基金(10871122
60671063)资助
关键词
分布时滞
HOPF分支
分支周期解
稳定性
distributed delay Hopf bifurcation periodic bifurcation solution stability
