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The water distribution system (WDS) is composed by several elements, where flow control is one of the most important components needed in order to provide a satisfactory level of service. In order to advene an adequate level of water in the distribution tanks, we need to dynamically control the flow. Here, we propose a replicator dynamics approach in order to control tanks, by allocating in them the...
A set of population equations with feedback control is studied. By applying comparison theorem of differential equation and constructing a suitable Lyapunov function, sufficient conditions for the permanence, strictly positive (component wise), global asymptotic stability of the positive equilibrium point are obtained. Some new results are obtained.
This article is concerned with the asymptotic stability of a class of nabla dynamic equations on time scales. By the use of Lyapunov direct method on time scales, some criteria on stability of the first-order linear dynamic equations are obtained, which extend the present results. The cobweb model is illustrated in the end.
It is important content that the studying connective stability among the stability studying of the large-scale interconnected systems. The many results recently have been given for the normal systems, the studying result of the singular large scale systems, however, is a little. The paper discussed the connective stability of a kind of nonlinear singular large-scale dynamical systems by means of singular...
The aim of this paper was to get a mathematical description on T cell-mediated cytolysis which we consider to be the dominant contributor of tumor regression, by studying a kinetic model of the effector cell response to cancer, which has been provided by R. P. Garay and R. Lefever. The methods employed were mathematical methods: differential analysis, Liapunov's method of stability, and linear systems...
The globally exponentially stabilizing control problem of a class of continuous-time bilinear systems is studied. For the systems, we give a nonlinear control. Under weaker premise than that in [1], the globally exponentially stability of the close-loop systems under the control is investigated by using Lyapunov's stability theory.
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