The role of incidence rate is very important in the study of epidemiological models. In this article, the analysis of an epidemic problem for the transmission dynamic of HBV with saturated incidence rate is presented, which is more generalize than bilinear incidence rate. After formulating the new mathematical model, the threshold quantity reproduction number [Formula: see text] is investigated...

This paper considers the globally asymptotic stabilization problem of multi-input multi-output bilinear systems with undamped natural response. Under the conditions for asymptotic stabilization by static state feedback control and system detectability, two output dynamic feedback controllers with saturation bounded control are constructed. The global asymptotic stability of the closed-loop syst...

in this paper, a new stage structured prey-predator model with linear functional response is proposed and studied. the stages for prey have been considered. the proposed mathematical model consists of three nonlinear ordinary differential equations to describe the interaction among juvenile prey, adult prey and predator populations. the model is analyzed by using linear stability analysis to ob...

Sufficient conditions for uniform global asymptotic stabilization of the origin are obtained for bilinear control systems with periodic coefficients. The proof is based on the use of the Krasovsky theorem on global asymptotic stability of the origin for periodic systems. The stabilizing control function is feedback control constructed as the quadratic form of the phase variables and depends on ...

The notion of geometric homogeneity is extended for differential inclusions. This kind of homogeneity provides the most advanced coordinate-free framework for analysis and synthesis of nonlinear discontinuous systems. The main qualitative properties of continuous homogeneous systems are extended to the discontinuous setting: the equivalence of the global asymptotic stability and the existence o...

Global asymptotic stability conditions for discrete nonlinear scalar stochastic systems with state delay are obtained based on the convergence theorem for semimartingale inequalities, without assuming the Lipschitz conditions for nonlinear drift functions. The Lyapunov-Krasovskii and degenerate functionals techniques are used. The derived stability conditions are directly expressed in terms of ...