In this paper, an SIR epidemic model with an infectious period and a non-linear Beddington-DeAngelis type incidence rate function is considered. The dynamics of this model depend on the reproduction number R0. Accurately, if R0 < 1, we show the global asymptotic stability of the disease-free equilibrium by analyzing the corresponding characteristic equation and using compa...

Purpose: Considering the influence of horizontal velocity on many biomechanical characteristics of walking, the purpose of this study was to investigate how inter-lower-limbs local and global asymmetry is influenced by changes in walking speed from slow to fast. Methods: Ground reaction force data and trajectory of attached markers of bilateral lower limbs of 15 right leg-dominant able-bodied ...

We consider a chemostat-type model in which a single species feeds on a limiting nutrient supplied at a constant rate. The model incorporates a general nutrient uptake function and two distributed (infinite) delays. The first delay models the fact that the nutrient is partially recycled after the death of the biomass by bacterial decomposition, and the second delay indicates that the growth of ...

Global finite-time observers are designed for a class of nonlinear systems that are uniformly observable and possibly non-Lipschitz. The non-Lipschitz conditions under which global finite-time observers exist are in terms of bounds of the varying rational powers of the increments of the non-Lipschitz nonlinearities. These are the same conditions under which semi-global finite-time observers wer...

Given a predesigned linear state feedback law for a linear plant ensuring (global) exponential stability of the linear closed loop, together with a certain level of performance, we address the problem of recovering (local or global) exponential stability and performance in the presence of plant input saturation and of a communication channel between the controller output and the saturated plant...

This paper is concerned with the convergence, global superconvergence, local superconvergence, and stability of collocation methods for u′ t au t bu t . The optimal convergence order and superconvergence order are obtained, and the stability regions for the collocation methods are determined. The conditions that the analytic stability region is contained in the numerical stability region are ob...

The main objective of this paper is to study the qualitative behavior for a class of nonlinear rational difference equation. We study the local stability, periodicity, Oscillation, boundedness, and the global stability for the positive solutions of equation. Examples illustrate the importance of the results Keywords— Difference equation, stability, oscillation, boundedness, globale stability an...

In the acquisition of skills requiring periodic body movements such as in cascade juggling, the establishment of stable body movements seems crucial. We investigated the processes of developing stable body movements in each of the three learning stages defined by the framework established by Beek and Van Santvoord (1992). We focused on two types of stability: stability of the body’s physical ce...