Asymptotic behavior of solutions of nonautonomous neutral dynamical systems

Producción CientíficaThis paper studies the dynamics of families of monotone nonautonomous neutral functional differential equations with nonautonomous operator, of great importance for their applications to the study of the long-term behavior of the trajectories of problems described by this kind of equations, such us compartmental systems and neural networks among many others. Precisely, more general admissible initial conditions are included in the study to show that the solutions are asymptotically of the same type as the coefficients of the neutral and non-neutral part.MICIIN/FEDER Grant RTI2018-096523-B-100H2020-MSCA-ITN-2014 643073 CRITICS

On Lyapunov-Krasovskii Functionals for Switched Nonlinear Systems with Delay

We present a set of results concerning the existence of Lyapunov-Krasovskii functionals for classes of nonlinear switched systems with time-delay. In particular, we first present a result for positive systems that relaxes conditions recently described in \cite{SunWang} for the existence of L-K functionals. We also provide related conditions for positive coupled differential-difference positive systems and for systems of neutral type that are not necessarily positive. Finally, corresponding results for discrete-time systems are described.Comment: 19 Page

Asymptotic constancy for pseudo monotone dynamical systems on function spaces

AbstractA pseudo monotone dynamical system is a dynamical system which preserves the order relation between initial points and equilibrium points. The purpose of this paper is to present some convergence, oscillation, and order stability criteria for pseudo monotone dynamical systems on function spaces for which each constant function is an equilibrium point. Some applications to neutral functional differential equations and semilinear parabolic partial differential equations with Neumann boundary condition are given

Classification of Some First Order Functional Differential Equations With Constant Coefficients to Solvable Lie Algebras

In this paper, we shall apply symmetry analysis to some first order functional differential equations with constant coefficients. The approach used in this paper accounts for obtaining the inverse of the classification. We define the standard Lie bracket and make a complete classification of some first order linear functional differential equations with constant coefficients to solvable Lie algebras.We also classify some nonlinear functional differential equations with constant coefficients to solvable Lie algebras

Optimal linear stability condition for scalar differential equations with distributed delay

Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote oscillations around steady states, and their stability depends on the particular shape of the delay distribution. Since in applications the mean delay is often the only reliable information available about the distribution, it is desirable to find conditions for stability that are independent from the shape of the distribution. We show here that for a given mean delay, the linear equation with distributed delay is asymptotically stable if the associated differential equation with a discrete delay is asymptotically stable. We illustrate this criterion on a compartment model of hematopoietic cell dynamics to obtain sufficient conditions for stability

Editorial for the special issue of axioms “Calculus of variations, optimal control and mathematical biology: a themed issue dedicated to professor Delfim F. M. Torres on the occasion of his 50th birthday”

No abstract available.publishe

Convergence for pseudo monotone semiflows on product ordered topological spaces

AbstractIn this paper, we consider a class of pseudo monotone semiflows, which only enjoy some weak monotonicity properties and are defined on product-ordered topological spaces. Under certain conditions, several convergence principles are established for each precompact orbit of such a class of semiflows to tend to an equilibrium, which improve and extend some corresponding results already known. Some applications to delay differential equations are presented

Existence and uniqueness of a periodic solution to a certain third-order neutral functional differential equation

In this paper, by applying Mawhin\u27s continuation theorem of the coincidence degree theory, some sufficient conditions for the existence and uniqueness of an (omega)-periodic solution for the following third-order neutral functional differential equation are established (dfrac{d^{3}}{dt^{3}}bigg ( x(t)-d(t)xbig (t-delta(t)big ) bigg )+a(t)ddot{x}(t)+b(t)fbig (t,dot{x}(t)big )+sum_{i=1}^{n}c_{i}(t)gbig (t,x(t-tau_{i}(t))big )=e(t)). Moreover, we present an example and a graph to demonstrate the validity of analytical conclusion