Abstract. This paper presents sufficient conditions which guarantee that the equilibrium of the damped harmonic oscillator x′′ + h(t)x′ + ωx = 0 is uniformly asymptotically stable, where h : [0,∞) → [0,∞) is locally integrable. These conditions work to suppress the rapid growth of the frictional force expressed by the integral amount of the damping coefficient h. The obtained sufficient conditi...

Tuberculosis (TB) is the leading cause of death among individuals infected with the human immunodeficiency virus (HIV). The study of the joint dynamics of HIV and TB present formidable mathematical challenges due to the fact that the models of transmission are quite distinct. Furthermore, although there is overlap in the populations at risk of HIV and TB infections, the magnitude of the proport...

We show that classically scale invariant gravity coupled to a single scalar field can undergo dimensional transmutation and generate an effective Einstein-Hilbert action for gravity, coupled to a massive dilaton. The same theory has an ultraviolet fixed point for coupling constant ratios such that all couplings are asymptotically free. However the catchment basin of this fixed point does not in...

Consider a system ẋ = f(x) + g(x)u (f and g locally Lipschitz) with the property that the associated autonomous system ż = f(z) has an asymptotically stable compactum C with region of attraction A. Assume that x is a solution of the former, defined on [0,∞), corresponding to an input function u. A simple proof is given of the following L -input converging-state property: if u ∈ L for some p ∈ [...

The basin of attraction of an asymptotically stable fixed point of the discrete dynamical system given by the iteration xn+1 = g(xn) can be determined through sublevel sets of a Lyapunov function. In [3] a Lyapunov function is constructed by approximating the solution of a difference equation using radial basis functions. However, the resulting Lyapunov function is non-local, i.e. it has no neg...

We present a study of the transfer of satellites between elliptic Keplerian orbits using Lyapunov stability theory specific to this problem. The construction of Lyapunov functions is based on the fact that a non-degenerate Keplerian orbit is uniquely described by its angular momentum and Laplace (Runge-Lenz) vectors. We suggest a Lyapunov function, which gives a feedback controller such that th...

finding a suitable estimation of stability domain around stable equilibrium points is an important issue in the study of nonlinear dynamical systems. this paper intends to apply a set of analytical-numerical methods to estimate the region of attraction for autonomous nonlinear systems. in mechanical and structural engineering, autonomous systems could be found in large deformation problems or c...

1 Department of Electromechanical Engineering, Centre for Aerospace Science and Technologies, UBI, University of Beira Interior, Calçada Fonte do Lameiro, 6201-001 Covilhã, Portugal 2 Scientific Area of Mathematics, ESTGV, Polytechnic Institute of Viseu, Campus Politécnico, 3504-510 Viseu, Portugal 3 Department of Mathematics and Applications, School of Sciences, Centre of Physics, University o...

Abstract -In this work we present a class of recurrent fashion. For example, the axons of the granule cells become networks which are asymptotically stable. For these networks, elongated and are arranged in parallel to each other forming the we discuss their similarity with certain structures in the central Parallel Fibers. Neurons from all the classes but granule cells, renervous system, and p...

In this study, we propose and analyse an extended SEIARD model with vaccination. We compute the control reproduction number $\mathcal{R}_c$ of our study stability equilibria. show that set disease-free equilibria is locally asymptotically stable when $\mathcal{R}_c<1$ unstable $\mathcal{R}_c>1$, provide a sufficient condition for its global stability. Furthermore, perform numerical simula...