arXiv subjects

César Silva

Publications and source records attributed to César Silva.

2 recordsLinked to original sources

arXiv2018

A consistent discrete version of a non-autonomous SIRVS model

A family of discrete non-autonomous SIRVS models with general incidence is obtained from a continuous family of models by applying Mickens non-standard discretization method. Conditions for the permanence and extinction of the disease and the stability of disease-free solutions are determined. The consistency of those discrete models with the corresponding continuous model is discussed: if the time step is sufficiently small, when we have extinction (respectively permanence) for the continuous model we also have extinction (respectively permanence) for the corresponding discrete model. Some numerical simulations are carried out to compare the different possible discretizations of our continuous model using real data.

math.DS↗

arXiv2009

Nonautonomous equations, generalized dichotomies and stable manifolds

Assuming the existence of a general nonuniform dichotomy for the evolution operator of a non-autonomous ordinary linear differential equation in a Banach space, we establish the existence of invariant stable manifolds for the semiflow generated by sufficiently small nonlinear perturbations of the linear equation. The family of dichotomies considered satisfies a general growth rate given by some increasing differentiable function, allows situations for which the classical Lyapunov exponents are zero, and contains the nonuniform exponential dichotomies as a very particular case. In addition we also give explicit examples of linear equations that admit all the possible considered dichotomies.

math.DS↗