Stability of Attractivity Regions for Autonomous Functional Differential Equations.
Stability of Caputo fractional differential equations by Lyapunov functions
The stability of the zero solution of a nonlinear nonautonomous Caputo fractional differential equation is studied using Lyapunov-like functions. The novelty of this paper is based on the new definition of the derivative of a Lyapunov-like function along the given fractional equation. Comparison results using this definition for scalar fractional differential equations are presented. Several sufficient conditions for stability, uniform stability and asymptotic uniform stability, based on the new...
Stability of higher order singular points of Poisson manifolds and Lie algebroids
We study the stability of singular points for smooth Poisson structures as well as general Lie algebroids. We give sufficient conditions for stability lying on the first-order approximation (not necessarily linear) of a given Poisson structure or Lie algebroid at a singular point. The main tools used here are the classical Lichnerowicz-Poisson cohomology and the deformation cohomology for Lie algebroids recently introduced by Crainic and Moerdijk. We also provide several examples of stable singular...
Stability of linear dynamic systems on time scales.
Stability of nonautonomous systems by Liapunov's direct method
This paper discusses asymptotic stability for nonautonomous systems by means of the direct method of Liapunov. The existence of a positive time-invariant Liapunov function with negative semi-definite derivative is assumed. The paper focuses on the extra conditions needed in order to guarantee asymptotic stability. The proposed criterion is compared with the standard results available for autonomous systems. A specialization and extension is obtained for a class of linear nonautonomous systems.
Stability of nonlinear systems under constantly acting perturbations.
Stability of operator semigroups: ideas and results
Stability of periodic or anti-periodic solutions of certain differential systems. (Stabilité des solutions périodiques ou anti-périodiques de certains systèmes différentiels.)
Stability of periodic solutions in extended Gierer-Meinhardt model.
Stability of perturbed delay homogeneous systems depending on a parameter
In this paper, we analyze the stability of homogeneous delay systems based on the Lyapunov Razumikhin function in the presence of a varying parameter. In addition, we show the stability of perturbed time delay systems when the nominal part is homogeneous.
Stability of solutions for an abstract Dirichlet problem
We consider continuous dependence of solutions on the right hand side for a semilinear operator equation Lx = ∇G(x), where L: D(L) ⊂ Y → Y (Y a Hilbert space) is self-adjoint and positive definite and G:Y → Y is a convex functional with superquadratic growth. As applications we derive some stability results and dependence on a functional parameter for a fourth order Dirichlet problem. Applications to P.D.E. are also given.
Stability of solutions of a nonstandard ordinary differential system by Lyapunov's second method.
Stability of the Endemic Coexistence Equilibrium for One Host and Two Parasites
For an SI type endemic model with one host and two parasite strains, we study the stability of the endemic coexistence equilibrium, where the host and both parasite strains are present. Our model, which is a system of three ordinary differential equations, assumes complete cross-protection between the parasite strains and reduced fertility and increased mortality of infected hosts. It also assumes that one parasite strain is exclusively vertically...
Stability problems for linear differential and difference systems
In this paper, there are derived sufficient conditions for exponential and asymptotic stability of differential and difference systems.
Stability properties of constrained jump-diffusion processes.
Stability properties of differential systems under constantly acting perturbations.
Stability properties of differential-algebraic equations and Spin-stabilized discretizations.
Stability rates for patchy vector fields
This paper is concerned with the stability of the set of trajectories of a patchy vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced in Ancona and Bressan (1999) to study feedback stabilization problems. For patchy vector fields in the plane, with polygonal patches in generic position, we show that the distance between a perturbed trajectory and an unperturbed one is of the same order of magnitude...
Stability rates for patchy vector fields
This paper is concerned with the stability of the set of trajectories of a patchy vector field, in the presence of impulsive perturbations. Patchy vector fields are discontinuous, piecewise smooth vector fields that were introduced in Ancona and Bressan (1999) to study feedback stabilization problems. For patchy vector fields in the plane, with polygonal patches in generic position, we show that the distance between a perturbed trajectory and an unperturbed one is of the same order of magnitude...
Stability results for a class of differential equation and application in medicine.