Browsing by Autor "Hugo Leiva"

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Qualitative analysis of a mathematical model about population of green turtles on the Galapagos island
(2021) Candy Herrera; Cosme Ramon Duque; Hugo Leiva
According to the IUCN, most sea turtles fall into one of the endangered categories. Since, sea turtles, like many other reptiles, present an unusual developmental process, marked by the determination of the sex of the offspring by environmental factors, more specifically by temperature. In the temperature sex determination (TSD) system the temperature of an embryo's environment during incubation period will dictate the embryo's sex development. This developmental process, together with the complex mating and nesting behavior and the vulnerability of sea turtles to threats of a natural or anthropogenic nature, naturally lead to the study of the population dynamics of the species.? For this reason, in this paper, we have developed a continuous model given by a system of three ordinary differential equations to study the dynamics of the green sea turtle population long-term, focusing the mathematical simulations on the data obtained for the nesting species of Galapagos Islands. Through the qualitative analysis of the model, the following is demonstrated: 1) The flow induced by the system is positively invariant on the region of biological interest and 2). The given condition on is necessary and sufficient for the unique nontrivial equilibrium point to be globally asymptotically stable in that region. When implementing the estimated values for our parameters in the numerical simulations, it was observed that indeed the population of Galapagos green sea turtles complies with the condition for which the nontrivial critical point is globally asymptotically stable.
Robustness of the controllability for the strongly damped wave equation under the influence of impulses, delays and nonlocal conditions
(National Polytechnic School, 2019) Hugo Leiva
This work proves the following conjecture: impulses, delays, and nonlocal conditions, under some assumptions, do not destroy some posed system qualitative properties since they are themselves intrinsic to it. we verified that the property of controllability is robust under this type of disturbances for the strongly damped wave equation. Specifically, we prove that the interior approximate controllability of linear strongly damped wave equation is not destroyed if we add impulses, nonlocal conditions and a nonlinear perturbation with delay in state. This is done by using new techniques avoiding fixed point theorems employed by A.E. Bashirov et al. In this case the delay help us to prove the approximate controllability of this system by pulling back the control solution to a fixed curve in a short time interval, and from this position, we are able to reach a neighborhood of the final state in time t by using that the corresponding linear strongly damped wave equation is approximately controllable on any interval {t0,T}, 0 < t0 < T.
Strongly convex set-valued maps
(Springer Science+Business Media, 2013) Hugo Leiva; Nelson Merentes; Kazimierz Nikodem; José L. Sánchez
We introduce the notion of strongly $$t$$ -convex set-valued maps and present some properties of it. In particular, a Bernstein–Doetsch and Sierpiński-type theorems for strongly midconvex set-valued maps, as well as a Kuhn-type result are obtained. A representation of strongly $$t$$ -convex set-valued maps in inner product spaces and a characterization of inner product spaces involving this representation is given. Finally, a connection between strongly convex set-valued maps and strongly convex sets is presented.