The stability of the positive fixed points of a discrete-time mathematical model for populations consisting of wild and genetically altered mosquitos proposed by Jia Li [1] is considered in this paper. The model is studied for proportional and constant mating rates. Under certain conditions the model with proportional mating rate has two positive fixed points, one unstable and the other locally...

Given a globally asymptotically controllable system, we derive from an existence theorem of a semiconcave control-Lyapunov function, the construction of a globally asymptotically stable feedback in the Euler sense. The feedback is rather regular in the case of control systems affine in the control. Abridged English Version In this paper, we study systems of the general form ẋ(t) = f(x(t), u(t))...

The dynamics of many epidemic models for infectious diseases that spread in a single host population demonstrate a threshold phenomenon If the basic reproduction number R is below unity the disease free equilibrium P is globally stable in the feasible region and the disease always dies out If R a unique endemic equilibrium P is globally asymptotically stable in the interior of the feasible regi...

We study a model of disease transmission with continuous age-structure for latently infected individuals and for infectious individuals. The model is very appropriate for tuberculosis. Key theorems, including asymptotic smoothness and uniform persistence, are proven by reformulating the system as a system of Volterra integral equations. The basic reproduction number R0 is calculated. For R0 < 1...

This paper is concerned with a cyclic predator-prey system with Sigmoidal type functional response. By using the differential inequality theory, some sufficient conditions are derived for the permanence of the system. By constructing a suitable Liapunov function, we obtain that the system has a unique asymptotically periodic solution which is globally asymptotically stable. Some numerical simul...

I ■V *■ • • • iV*TC | V j j J j (1.1) x'=/(x) in which f(x) is of class C1 on En. Let J(x) = (df/dx) denote the Jacobian matrix of /and let H(x) = (J+J*)/2 be the symmetric part of J(x). One of the results of [2] is to the effect that if (1.2) /(0) = 0 and (1.3) H(x) is negative definite (for fixed x ^ 0), then x = 0 is a globally asymptotically stable solution of (1.1); i.e., every solution x ...

Abstract. We study the global stability of two models for the HIV virus dynamics, that take into account the CTL immune response and antigenic variation. We show that both models are globally asymptotically stable, by using appropriate Lyapunov functions. For both models, we characterise the stable equilibrium points for the entire biologically relevant parameter range. In the model with antige...

The robust stabilization problem of chaos suppression for permanent magnet synchronous motors (PMSM) drive system is investigated in presence of parametric uncertainties. Based on control Lyapunov function (CLF) approach, a new state feedback controller is designed to realize the state of the system globally asymptotically stable. The stability of the proposed control scheme is verified via Lya...