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global Dynamics for an HIV Infection Model with Crowley-Martin Functional Response and Two Distributed Delays

Journal of Systems Science & Complexity 2018年第2期31卷 385-395页

作者： LIU Yongqi WU Chunsong College of Applied Mathematics Beijing Normal University Zhuhai 519087 China College of Mathematics and Information Science Henan Normal University Xinxiang 453007 China.

In this paper, an HIV dynamics model with two distributed intracellular delays incorporating Crowley-Martin functional response infection rate is investigated. The authors take into account multiple stage disease transmission and the latently infected cells（not yet producing virus） in our system. The authors consider nonnegativity, boundedness of solutions, and global asymptotic stability of the system. By constructing suitable Lyapunov functionals and using the Lyapunov-La Salle invariance principle, the authors prove the global stability of the infected（endemic） equilibrium and the diseasefree equilibrium for time delays. The authors have proven that if the basic reproduction number R_0 is less than unity, then the disease-free equilibrium is globally asymptotically stable, and if R_0 is greater than unity, then the infected equilibrium is globally asymptotically stable. The results obtained show that the global dynamic behaviors of the model are completely determined by the basic reproduction number R_0 and that the time delay does not affect the global asymptotic properties of the model.

关键词： Crowley-Martin functional response distributed delays global stability analysis HIV model.

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Instability of cylinder wake under open-loop active control

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Applied Mathematics and Mechanics(English Edition) 2017年第3期38卷 439-452页

作者： Yadong HUANG Benmou ZHOU Zhaolie TANG Science and Technology on Transient Physics Laboratory Nanjing University of Science and Technology Nanjing 210094 China

Instability of a wake controlled by a streamwise Lorentz force is investigated through a Floquet stability analysis. The streamwise Lorentz force, which is a two-dimensional control input created by an electromagnetic actuator located on the cylinder surface,adjusts the base flow to affect the three-dimensional wake instability and achieve wake stabilization and transition delay. The instability mode at a Reynolds number Re = 300 can be transformed from B to A with N = 1.0, where N is an interaction number representing the strength of the Lorentz force relative to the inertial force in the fluid. The wake flow is Floquet stable when N increases to 1.3. The spanwise perturbation wavelengths are 3.926 D and 0.822 D in the modes A and B, respectively, where D is the cylinder diameter. In addition, the oscillating amplitudes of drag and lift are reduced with the increase in the interaction number. Particle tracing is used to explore the essential physical mechanism for mode transformation. The path lines show that suppression of flow separation hinders the fluid deformation and rotation, leading to the decrease in elliptic and hyperbolic instability regions, which is the material cause of mode *** of the results indicate that wake stabilization and transition delay can be achieved under open-loop active control via the streamwise Lorentz force.

关键词： flow instability global stability analysis open-loop active control streamwise Lorentz force wake stabilization transition delay

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