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Hybrid control of delay induced hopf bifurcation of dynamical small-world network

机译:动态小世界网络的时延霍夫分支的混合控制

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摘要

In this paper, we focus on the Hopf bifurcation control of a small-world network model with time-delay. With emphasis on the relationship between the Hopf bifurcation and the time-delay, we investigate the effect of time-delay by choosing it as the bifurcation parameter. By using tools from control and bifurcation theory, it is proved that there exists a critical value of time-delay for the stability of the model. When the time-delay passes through the critical value, the model loses its stability and a Hopf bifurcation occurs. To enhance the stability of the model, we propose an improved hybrid control strategy in which state feedback and parameter perturbation are used. Through linear stability analysis, we show that by adjusting the control parameter properly, the onset of Hopf bifurcation of the controlled model can be delayed or eliminated without changing the equilibrium point of the model. Finally, numerical simulations are given to verify the theoretical analysis.
机译:在本文中,我们关注具有时滞的小世界网络模型的Hopf分支控制。着眼于Hopf分支与时间延迟之间的关系,我们通过选择时间作为分支参数来研究时间延迟的影响。利用控制和分岔理论中的工具,证明存在一定的时滞临界值,对于模型的稳定性。当时间延迟超过临界值时,模型将失去稳定性,并发生Hopf分支。为了提高模型的稳定性,我们提出了一种改进的混合控制策略,其中使用了状态反馈和参数摄动。通过线性稳定性分析,我们表明,通过适当地调整控制参数,可以在不更改模型平衡点的情况下延迟或消除受控模型的Hopf分叉的发作。最后,通过数值模拟验证了理论分析。

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