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首页> 外文期刊>Physical review, E >Constructing Hopf bifurcation lines for the stability of nonlinear systems with two time delays
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Constructing Hopf bifurcation lines for the stability of nonlinear systems with two time delays

机译：构建Hopf分岔线，有两个时间延迟的非线性系统稳定性

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摘要

Although the plethora real-life systems modeled by nonlinear systems with two independent time delays, the algebraic expressions for determining the stability of their fixed points remain the Achilles' heel. Typically, the approach for studying the stability of delay systems consists in finding the bifurcation lines separating the stable and unstable parameter regions. This work deals with the parametric construction of algebraic expressions and their use for the determination of the stability boundaries of fixed points in nonlinear systemswith two independent time delays. In particular, we concentrate on the cases for which the stability of the fixed points can be ascertained from a characteristic equation corresponding to that of scalar two-delay differential equations, one-component dual-delay feedback, or nonscalar differential equations with two delays for which the characteristic equation for the stability analysis can be reduced to that of a scalar case. Then, we apply our obtained algebraic expressions to identify either the parameter regions of stable microwaves generated by dual-delay optoelectronic oscillators or the regions of amplitude death in identical coupled oscillators.
机译：虽然由具有两个独立时间延迟的非线性系统建模的血清真实系统，但是用于确定其固定点的稳定性的代数表达仍然是Achilles的脚跟。通常，用于研究延迟系统的稳定性的方法包括找到分离稳定和不稳定的参数区域的分叉线。这项工作涉及代数表达的参数结构及其用于确定非线性系统中的固定点的稳定边界的两个独立时间延迟。特别是，我们专注于可以从对应于标量的双延迟微分方程，单组分双延迟反馈或具有两个延迟的非卡拉微分方程对应的特征方程来确定固定点的稳定性的情况可以减少稳定性分析的特性方程，可以减少到标量案例。然后，我们应用所获得的代数表达式以识别由双延迟光电子振荡器或相同耦合振荡器中的振幅死亡区域产生的稳定微波的参数区域。

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