GENERALISED LYAPUNOV-RAZUMIKHIN TECHNIQUES FOR SCALAR STATE-DEPENDENT DELAY DIFFERENTIAL EQUATIONS

F. M. G. MAGPANTAY; A. R. HUMPHRIES

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GENERALISED LYAPUNOV-RAZUMIKHIN TECHNIQUES FOR SCALAR STATE-DEPENDENT DELAY DIFFERENTIAL EQUATIONS

机译：标量依赖延迟微分方程的广义Lyapunov-Razumikhin技术

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摘要

We present generalised Lyapunov-Razumikhin techniques for establishing global asymptotic stability of steady-state solutions of scalar delay differential equations. When global asymptotic stability cannot be established, the technique can be used to derive bounds on the persistent dynamics. The method is applicable to constant and variable delay problems, and we illustrate the method by applying it to the state-dependent delay differential equation known as the sawtooth equation, to find parameter regions for which the steady-state solution is globally asymptotically stable. We also establish bounds on the periodic orbits that arise when the steady-state is unstable. This technique can be readily extended to apply to other scalar delay differential equations with negative feedback.

机译：我们呈现了广义Lyapunov-Razumikhin技术，用于建立标量延迟微分方程稳态解的全局渐近稳定性。当无法建立全局渐近稳定性时，该技术可用于导出持久性动态的界限。该方法适用于恒定和可变的延迟问题，我们通过将其应用于称为锯齿道方程的状态依赖延迟微分方程来说明该方法，以找到稳态解决方案的参数区域全局渐近稳定。我们还在稳态不稳定时产生的周期性轨道上的界限。可以容易地扩展该技术以应用于具有负反馈的其他标量延迟微分方程。

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来源
《Discrete and continuous dynamical systems▼hSeries S》 |2020年第1期|85-104|共20页
作者
F. M. G. MAGPANTAY; A. R. HUMPHRIES;
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作者单位

Department of Mathematics and Statistics Queen's University Kingston ON Canada K7L 3N6;

Department of Mathematics and Statistics McGill University Montreal QC Canada H3A 0B9;

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正文语种 eng
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关键词
Delay differential equations; Lyapunov-Razumikhin; state-dependent delays; global asymptotic stability;

机译：延迟微分方程;Lyapunov-Razumikhin;国家依赖的延误;全球渐近稳定性;

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1. DECAY AND GROWTH RATES OF SOLUTIONS OF SCALAR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY AND STATE-DEPENDENT NOISE [J] . JOHN A. D. APPLEBY Stochastics and dynamics . 2005,第2期

机译：具有无界时滞和状态相关噪声的标量随机时滞微分方程解的衰减率和增长率
2. Resonance Phenomenaina Scalar Delay Differential Equation with Two State-Dependent Delays [J] . Calleja R. C., Humphries A. R., Krauskopf B. SIAM journal on applied dynamical systems . 2017,第3期

机译：具有两个状态依赖延迟的谐振现象标量延迟微分方程
3. A regularization for discontinuous differential equations with application to state-dependent delay differential equations of neutral type [J] . Fusco G., Guglielmi N. Journal of Differential Equations . 2011,第7期

机译：不连续微分方程的正则化及其在依赖状态的中立型时滞微分方程中的应用
4. Identification of Parameters in Neutral Functional Differential Equations with State-Dependent Delays [C] . Ferenc Hartung, Janos Turi, The Institute of Electrical and Electronics EngineersInc. IEEE Conference on Decision and Control . 2005

机译：具有状态依赖延迟中性功能微分方程参数的识别
5. Differential equations with state-dependent delay: Global Hopf bifurcation and smoothness dependence on parameters. [D] . Hu, Qingwen. 2008

机译：具有状态相关延迟的微分方程：全局Hopf分叉和平滑度对参数的依赖。
6. A new multi-step technique with differential transform method for analytical solution of some nonlinear variable delay differential equations [O] . Brahim Benhammouda, Hector Vazquez-Leal -1

机译：微分变换方法的一种新的多步技术用于求解某些非线性可变时滞微分方程的解析解
7. Resonance phenomena in a scalar delay differential equation with two state-dependent delays [O] . Calleja, R. C., Humphries, A. R., Krauskopf, B. 2017

机译：具有两个标量延迟微分方程的共振现象与状态有关的延误
8. Estimation of Time- and State-Dependent Delays and Other Parameters in Functional Differential Equations [R] . Murphy, K. A. 1988

机译：泛函微分方程中时间和状态依赖时滞及其他参数的估计

GENERALISED LYAPUNOV-RAZUMIKHIN TECHNIQUES FOR SCALAR STATE-DEPENDENT DELAY DIFFERENTIAL EQUATIONS

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