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This paper investigates robust stability of genetic regulatory networks with distributed delay. Different from other papers,
distributed delay is induced. It says that the concentration of macromolecule depends on an integral of the regulatory function
of over a specified range of previous time, which is more realistic. Based on Lyapunov stability theory and linear matrix
inequality (LMI), sufficient conditions for genetic regulatory networks to be global asymptotic stability and robust stability
are derived in terms of LMI. Two numerical examples are given to illustrate the effectiveness of our theoretical results. 相似文献
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Michel C. Delfour André Garon 《Computer methods in biomechanics and biomedical engineering》2013,16(1):19-34
The notion of dose that comes from the biologists has been introduced by Delfour et al. (2005 SIAM J. Appl. Math. 65(3):858–881) in the context of coated stents to control restenosis. Assuming a stationary velocity profile of the blood flow in the lumen, it leads to a time-independent equation for the dose that considerably simplifies the analysis and the design problem. Under stable conditions the blood flow is pulsative, that is the velocity field can be assumed to be periodic. So it is necessary to justify the replacement of the periodic field by its time average over the pulsation period. In this paper, firstly we introduce the new unfolded dose and its equations without a priori constraint on the size of the period. So it can be used in biochemical problems where the period is large compared to the time constants of the system. Secondly, we show that, as the period goes to zero, the velocity field can be replaced by its average over the period. Numerical tests on a one-dimensional example are included to illustrate the theory. 相似文献
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《Journal of biological dynamics》2013,7(6):635-647
In this paper, we consider a simple chemostat model involving two obligate mutualistic species feeding on a limiting substrate. Systems of differential equations are proposed as models of this association. A detailed qualitative analysis is carried out. We show the existence of a domain of coexistence, which is a set of initial conditions in which both species survive. We demonstrate, under certain supplementary assumptions, the uniqueness of the stable equilibrium point which corresponds to the coexistence of the two species. 相似文献
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Even Tjørve 《Journal of Biogeography》2003,30(6):827-835
Aim This paper reviews possible candidate models that may be used in theoretical modelling and empirical studies of species–area relationships (SARs). The SAR is an important and well‐proven tool in ecology. The power and the exponential functions are by far the models that are best known and most frequently applied to species–area data, but they might not be the most appropriate. Recent work indicates that the shape of species–area curves in arithmetic space is often not convex but sigmoid and also has an upper asymptote. Methods Characteristics of six convex and eight sigmoid models are discussed and interpretations of different parameters summarized. The convex models include the power, exponential, Monod, negative exponential, asymptotic regression and rational functions, and the sigmoid models include the logistic, Gompertz, extreme value, Morgan–Mercer–Flodin, Hill, Michaelis–Menten, Lomolino and Chapman–Richards functions plus the cumulative Weibull and beta‐P distributions. Conclusions There are two main types of species–area curves: sample curves that are inherently convex and isolate curves, which are sigmoid. Both types may have an upper asymptote. A few have attempted to fit convex asymptotic and/or sigmoid models to species–area data instead of the power or exponential models. Some of these or other models reviewed in this paper should be useful, especially if species–area models are to be based more on biological processes and patterns in nature than mere curve fitting. The negative exponential function is an example of a convex model and the cumulative Weibull distribution an example of a sigmoid model that should prove useful. A location parameter may be added to these two and some of the other models to simulate absolute minimum area requirements. 相似文献
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研究了具有反馈控制和功能性反应的两种群竞争系统.通过构造适当的Lyapunov函数,得到了系统存在全局渐进稳定的概周期解的充分性条件。 相似文献