Dynamical analysis of a delayed six‐neuron BAM network

In this article, a simplified bidirectional associative memory network with delays involving six neurons is considered. By analyzing the distribution of roots of the characteristic equation for linearized system regarding the sum of delay as a bifurcation parameter, we obtain the condition of the occurrence for Hopf bifurcation. It reveals that Hopf bifurcation occurs when the sum of the delay passes through a critical value. The direction and the stability of the bifurcating periodic solution are determined by applying the normal form theory and center manifold theorem. Finally, a numerical example is used to illustrate the validity of theoretical results obtained. © 2015 Wiley Periodicals, Inc. Complexity 21: 9–28, 2016     

Dynamics and control in an $$({\varvec{n}}+{\varvec{2}})$$ ( n + 2 ) -neuron BAM network with multiple delays

Nonlinear Dynamics - The issues of the stability and bifurcation for a delayed BAM network involving two neurons in the I-layer and arbitrary neurons in the J-layer are concerned in the present...     

反馈时滞对van der Pol振子张弛振荡的影响

研究反馈控制环节时滞对van derPol振子张弛振荡的影响. 首先, 通过稳定性切换分析, 得到了系统的慢变流形的稳定性和分岔点分布图, 结果表明, 当时滞大于某临界值时, 系统慢变流形的结构发生本质的变化.其次, 基于几何奇异摄动理论, 分析了慢变流形附近解轨线的形状, 发现时滞反馈会引起张弛振荡中的慢速运动过程中存在微幅振荡, 其中微幅振荡来自于内部层引起的振荡和Hopf分岔产生的振荡两个方面; 同时, 时滞对张弛振荡的周期也具有显著的影响. 实例分析表明理论分析结果与数值结果相吻合.      

Novel design for bifurcation control in a delayed fractional dual congestion model

This letter puts forward an ingenious feedback control method with parametric delay to manipulate bifurcation control for a delayed fractional dual congestion model. By employing time delay as a bifurcation parameter, the local dynamics involving stability and Hopf bifurcation is examined. The control efforts can be realized with or without time delay in the strength of feedback control. It suggests that the stability performance is consumedly elevated by exploiting the parametric delay feedback controller, yet Hopf bifurcation engenders ahead of time in the event of the absence of the controller. Moreover, the impact of the order or linear feedback gain on the bifurcation point is numerically discussed via aborative calculation. Numerical simulations are eventually actualized to corroborate the proposed scheme.