In this paper, the works on the stability problem for singularly perturbed systems are extended to include the factors of uncertainties and time delays, which often cause the instability of the systems. The properties of ∞ H -norm are used throughout this paper to derive the robust stability criterion. A frequency-domain sufficient condition for the asymptotic stability of the slow subsystem (r...

We investigate a class of multigroup dengue epidemic model. We show that the global dynamics are determined by the basic reproductive number R0. We present that when R0 ≤ 1, there is a unique disease-free equilibrium which is globally asymptotically stable; when R0 > 1, there exists a unique endemic equilibrium and it is globally asymptotically stable proved by a graph-theoretic approach to the...

In this paper, we consider global stability for a heroin model with two distributed delays. The basic reproduction number of the heroin spread is obtained, which completely determine the stability of equilibria. Using the direct Lyapunov method with Volterra type Lyapunov function, we show that the drug use-free equilibrium is globally asymptotically stable if the basic reproduction number is l...

We establish robustness stability results for a specific type of artificial neural networks for associative memories under parameter perturbations and determine conditions that ensure the existence of asymptotically stable equilibria of the perturbed neural system that are the asymptotically stable equilibria of the original unperturbed neural network. The proposed stability analysis tool is th...

*Correspondence: [email protected] 1Department of Mathematics, Xinjiang Institute of Engineering, Urumqi, Xinjiang 830091, P.R. China Full list of author information is available at the end of the article Abstract In this paper, a diffusive and delayed virus dynamics model with Crowley-Martin incidence function and CTL immune response is investigated. By constructing the Lyapunov functionals...

* 0-7803-7952-7/03/$17.00 © 2003 IEEE Abstract In this paper, the robust stability problem for a class of uncertain two-time-scale neutral systems subject to unstructured perturbations is investigated. The properties of ∞ H -norm are used throughout this paper to derive the robust stability criterion. A frequency-domain delay-dependent criterion for the asymptotic stability of the slow neutral ...

This paper studies a two-legged kneed walking robot with point feet. At any given moment, only one foot is in contact with the ground, and the switching is instantaneous. The robot can be considered as a simpli ed model of human walking. The periodic torque histories applied to each link are a priori prescribed for a motion and are not changed by any feedback interference. Nevertheless the robo...

A class of autocatalytic reaction networks based on template-dependent replication and specific catalysis is considered. Trimolecular "elementary steps" of simple replicator dynamics are resolved into two consecutive irreversible reactions. The extreme cases, competition for common resources and hypercycle-like cooperative feedback, were analyzed in some detail. Although the dynamics of the ext...

Stability is often the goal for clearinghouses in matching markets, such as those matching residents to hospitals, students to schools, etc. Stable outcomes absent transfers need not be utilitarian effi cient, suggesting the potential value of transfers. We study the wedge between stability and effi ciency in large one-to-one matching markets. We show stable matchings are effi cient asymptotica...

In this note, the problem of control for a class of chaotic systems is studied. Only partial information of the systems states is known. First, an adaptive observer is designed to ensure the corresponding error system asymptotically stable. Then, based on the states obtained by the above observer, a nonlinear state feedback controller is constructed for the chaotic system, which, according to t...