2.In this paper,we give a Hopf bifurcation diagram for liénard equation with delay in the r- K parameter plane.本文在 r-K 参数平面上给出时滞 Liénard 方程的 Hopf 分支图,并用简化后的时滞 liénard 方程 Hopf 分支公式指出,当以 K 为分支参数时,其 Hopf 分支在分支值 K=K_0左右两侧都有可能...
- D decomposition, one can determine the stability domain of the equilibrium and Hopf bifurcation curves in the parameter space.潘家齐唐明微分方程年刊:英文版Pan Jiaqi and Tang Ming.Hopf bifurcation diagram of time-delay Lienard equation Ann. of Diff. Eqs . 2003Pan Jiaqi and Tang Ming.Hopf ...
In this paper a new approach is proposed to 目前普遍认为 Hopf 分岔是导致电力系统电压 solve Hopf bifurcation point of dynamic voltage stability by 失稳的 3 种分岔形式之一,而求解 Hopf 分岔点成 reduced order, and the feature of the proposed approach is to 为动态电压稳定分析的重要内容。 reduce ...
The Hopf bifurcation analysis of the system has been done using center manifold theorem for \\sigma = -1; r > 1. Phase portraits of solutions of the system are plotted for various system parameters to substantiate the change in dynamics. The bifurcation diagram and the Lyapunov exponent ...
5)the algorithm of the HOPF bifurcation theorem by using graph图解HOPF算法 6)Complete graph Hopf algebra完全图Hopf代数
Thus, a bifurcation diagram is a graphical representation of the bifurcations in terms of the control parameters [6]. Although there are many different kinds of bifurcations [6], [7], [8], in this work, we focus on Hopf bifurcations (HB). The term Hopf Bifurcation, also known Poincaré...
time delaydelay Lienard equationsvan der Pol equationsHopf bifurcationperiod-doubling bifurcationStarting from the delay Li茅nard and van der Pol equations ... X Jian,KW Chung - 《Chaos Solitons & Fractals》 被引量: 82发表: 2009年 HOPFBIFURCATIONDIAGRAMOFTIME-DELAYLI NARDEQUATION In this paper,...
关键词:食物链;合作捕食;稳定性;Hopf 分支;数值模拟 中图分类号:O 175.26 文献标志码 :A 文章编号 :1008⁃9497(2023)05⁃539⁃12 HAN Wanqin, SHI Yao, BAO Xiongxiong( College of Science,Chang′an University,Xi ′an 710064,China) Hopf bifurcation of a food chain model with cooperative ...
The bifurcation point is determined. Center manifold theory is proposed to reduce the system dimension,and then a three-order normal form of Hopf bifurcation is calculated by plotting the bifurcation diagram. In addition,the effect of the bifurcation parameter on the swing of the limit cycle is ...
Finally, we give the bifurcation diagram with numerical illustration, showing that the pair of stable small-amplitude periodic solutions can also exist in a large region of unfolding parameters, and the financial system with delay can exhibit chaos via period-doubling bifurcations as the unfolding ...