Robust uniform persistence in discrete and continuous nonautonomous systems

Salceanu P.L.

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Robust uniform persistence in discrete and continuous nonautonomous systems

机译：离散和连续非自治系统中的鲁棒一致持久性

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This is an extension of the work in Salceanu (2011) [14] to nonautonomous systems of difference and differential equations on the positive cone of R ~m that exhibit a positively invariant boundary hyperplane X. It is shown that when a compact subset of X, which attracts all orbits in X, is a robust uniform weak repeller, robust uniform persistence for the complementary dynamics (i.e., the dynamics in R ~m{set minus} X) is obtained. Additional assumptions are made, to deal with the nonautonomous nature of the systems. Some particular cases that often occur in applications are discussed and then sufficient conditions for the robust uniform persistence of the disease in two epidemic models from the literature are given.

机译：这是Salceanu（2011）[14]中的工作的扩展，它扩展到R〜m正圆锥上具有正不变边界超平面X的非自治差分和微分方程组。研究表明，当X的紧凑子集时，它吸引了X中的所有轨道，是一个鲁棒的均匀弱推斥极，获得了互补动力学（即，R〜m {set减去X}中的动力学）的鲁棒均匀持久性。进行了其他假设，以处理系统的非自治性质。讨论了在应用中经常发生的一些特殊情况，然后在文献中的两个流行病模型中给出了足以使该疾病稳定，持久持续的充分条件。

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《Journal of Mathematical Analysis and Applications》 |2013年第2期|共14页
作者
Salceanu P.L.;
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正文语种 eng
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Difference and differential equations; Disease persistence; Epidemic models; Lyapunov exponents; Nonautonomous systems; Robust uniform persistence;

机译：差分和微分方程;疾病持久性;流行病模型;Lyapunov指数;非自治系统;鲁棒一致持久性;

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1. Robust uniform persistence in discrete and continuous nonautonomous systems [J] . Salceanu P.L. Journal of Mathematical Analysis and Applications . 2013,第2期

机译：离散和连续非自治系统中的鲁棒一致持久性
2. Robust uniform persistence and competitive exclusion in a nonautonomous multi-strain SIR epidemic model with disease-induced mortality [J] . A. S. Ackleh, P. L. Salceanu Journal of Mathematical Biology . 2014,第1a2期

机译：在具有疾病引起的死亡率的非自主多菌株SIR流行病模型中的鲁棒一致持久性和竞争排斥
3. Uniform persistence for nonautonomous and random parabolic Kolmogorov systems [J] . Mierczynski J, Shen WX, Zhao XQ Journal of Differential Equations . 2004,第2期

机译：非自治和随机抛物线Kolmogorov系统的一致持久性
4. MODEL VALIDATION FOR ROBUST CONTROL OF UNCERTAIN CONTINUOUS-TIME SYSTEMS WITH DISCRETE AND CONTINUOUS MEASUREMENTS [C] . Andrey V. Savkin, Ian R. Petersen Proceedings of the 13th world congress . 1997

机译：离散和连续测量不确定连续系统的鲁棒控制模型验证
5. Analysis and robust control of hybrid continuous/discrete time systems. [D] . Bamieh, Bassam Abbas. 1992

机译：混合连续/离散时间系统的分析和鲁棒控制。
6. A Robust Computational Technique for Model Order Reduction of Two-Time-Scale Discrete Systems via Genetic Algorithms [O] . Othman M. K. Alsmadi, Zaer S. Abo-Hammour 2015

机译：基于遗传算法的两尺度离散系统模型降阶的鲁棒计算技术
7. DIGITAL CONTROL SYSTEMS IMPLEMENTATION TECHNIQUES, VOLUME 70 OF CONTROL AND DYNAMIC SYSTEMS: ADVANCES IN THEORY AND APPLICATIONS, C. Leondes (ed), Academic Press, San Diego, 1995, 390 pp., ISBN 0-12-0127702, $99.00 DISCRETE-TIME CONTROL SYSTEM ANALYSIS AND DESIGN, VOLUME 71 OF CONTROL AND DYNAMIC SYSTEMS: ADVANCES IN THEORY AND APPLICATIONS, C. Leondes (ed), Academic Press, San Diego, 1995, 410 pp., ISBN 0-12-0127715, $99.00 DISCRETE-TIME CONTROL SYSTEM IMPLEMENTATION TECHNIQUES, VOLUME 72 OF CONTROL AND DYNAMIC SYSTEMS: ADVANCES IN THEORY AND APPLICATIONS, C. Leondes (ed), Academic Press, San Diego, 1995, 388 pp., ISBN 0-12-0127725, $99.00 TECHNIQUES IN DISCRETE-TIME STOCHASTIC CONTROL SYSTEMS, VOLUME 73 OF CONTROL AND DYNAMIC SYSTEMS: ADVANCES IN THEORY AND APPLICATIONS, C. Leondes (ed), Academic Press, San Diego, 1995, 380 pp., ISBN 0-12-0127734, $99.00 TECHNIQUES IN DISCRETE AND CONTINUOUS ROBUST SYSTEMS, VOLUME 74 OF CONTROL AND DYNAMIC SYSTEMS: ADVANCES IN THEORY AND APPLICATIONS, C. Leondes (ed), Academic Press, San Diego, 1995, 412 pp., ISBN 0-12-0127741, $99.00 [O] . D. SUBBARAM NAIDU 1997

机译：数字控制系统的实施技术，控制和动态系统的第70卷：理论和应用的进步，C.丝丝（ED），学术出版社，圣地亚哥，1995,390 PP，ISBN 0-12-0127702，99.00美元离散时间控制系统分析和设计，控制和动态系统的第71卷：理论和应用的进步，C.丝丝（ED），学术出版社，圣地亚哥，1995,410 PP，ISBN 0-12-0127715，99.00美元离散时间控制系统实现技术，控制和动态系统的第72卷：理论和应用的进步，C.丝丝（ED），学术出版社，圣地亚哥，1995,388 pp，ISBN 0-12-0127725，99.00美元的离散 - 时间随机控制系统，控制和动态系统的VOLUME 73：前进，理论与应用，C Leondes（ED），学术出版社，圣地亚哥，1995年，380页，ISBN 0-12-0127734，在离散和$ 99.00技术。连续稳健的系统，控制和动态系统的第74卷：理论和应用的进步，C. leondes（ed），学术出版社，圣地亚哥，1995,412 pp。，ISBN 0-12-0127741，99.00美元

Robust uniform persistence in discrete and continuous nonautonomous systems

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