arXiv subjects

Víctor M. Villarragut

Publications and source records attributed to Víctor M. Villarragut.

3 recordsLinked to original sources

arXiv2024

Exponential Ordering for Neutral Functional Differential Equations With Non-Autonomous Linear D-Operator

We study neutral functional differential equations with stable linear non-autonomous $D$-operator. The operator of convolution $\hat{D}$ transforms $BU$ into $BU$. We show that, if $D$ is stable, then $\hat{D}$ is invertible and, besides, $\hat{D}$ and $\hat{D}^{-1}$ are uniformly continuous for the compact-open topology on bounded sets. We introduce a new transformed exponential order and, under convenient assumptions, we deduce the 1-covering property of minimal sets. These conclusions are applied to describe the amount of material in a class of compartmental systems extensively studied in the literature.

math.DS↗

arXiv2024

Exponential Ordering for Nonautonomous Neutral Functional Differential Equations

We study monotone skew-product semiflows generated by families of nonautonomous neutral functional differential equations with infinite delay and stable D-operator, when the exponential ordering is considered. Under adequate hypotheses of stability for the order on bounded sets, we show that the omega-limit sets are copies of the base to explain the long-term behavior of the trajectories. The application to the study of the amount of material within the compartments of a neutral compartmental system with infinite delay, shows the improvement with respect to the standard ordering.

math.DS↗

arXiv2023

Attractors In Almost Periodic Nicholson Systems And Some Numerical Simulations

The existence of a global attractor is proved for the skew-product semiflow induced by almost periodic Nicholson systems and new conditions are given for the existence of a unique almost periodic positive solution which exponentially attracts every other positive solution. Besides, some numerical simulations are included to illustrate our results in some concrete Nicholson systems.

math.DS↗