A constructive method for time-varying stabilization of smooth driftless controllable systems is developed. It provides time-varying homogeneous feedback laws that are continuous and smooth away from the origin. These feedbacks make the closed-loop system globally exponentially asymptotically stable if the control system is homogeneous with respect to a family of dilations and, using local homo...

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 weakly uniformly globally asymptotically stable closed (not necessarily compact) set A for a differential inclusion that is defined on Rn, is locally Lipschitz on Rn\A, and satisfies other basic conditions, we construct a weak Lyapunov function that is locally Lipschitz on Rn. Using this result, we show that uniform global asymptotic controllability to a closed (not necessarily compact)...

This paper considers a non-linear mathematical model for HIV epidemic that spreads in a variable size population through both horizontal and vertical transmission. The equilibrium points of the model system are found and their stability is investigated. The model exhibits two equilibria namely, the disease-free and the endemic equilibrium. It is found that if the basic reproduction number R0 < ...

Human habitat connectivity, movement rates, and spatial heterogeneity have tremendous impact on malaria transmission. In this paper, a deterministic system of differential equations for malaria transmission incorporating human movements and the development of drug resistance malaria in an [Formula: see text] patch system is presented. The disease-free equilibrium of the model is globally asympt...

in this article, we survey the asymptotic stability analysis of fractional differential systems with the prabhakar fractional derivatives. we present the stability regions for these types of fractional differential systems. a brief comparison with the stability aspects of fractional differential systems in the sense of riemann-liouville fractional derivatives is also given.

either stable or unstable with respect to small perturbations away from the steady state. If all small perturbations (in any direction in the n-dimensional state space of the reaction network) eventually return to x, then this steady state is said to be (locally asymptotically) stable. If there exist small perturbations (in some particular directions in state space) that depart from x and never...