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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...
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.
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.
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.
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...
In this paper, there are derived sufficient conditions for exponential and asymptotic stability of differential and difference systems.
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...
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...
A suitable Liapunov function is constructed for proving that the unique critical point of a non-linear system of ordinary differential equations, considered in a well determined polyhedron , is globally asymptotically stable in . The analytic problem arises from an investigation concerning a steady state in a particular macromolecular system: the visual system represented by the pigment rhodopsin in the presence of light.
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