On the gamma-logistic map and applications to a delayed neoclassical model of economic growth

This is a post-peer-review, pre-copyedit version of an article published in Nonlinear Dynamics. The final authenticated version is available online at: https://doi.org/10.1007/s11071-019-04785-1In this work, we study the stability properties of a delay differential neoclassical model of economic growth, based on the original model proposed by Solow (Q J Econ 70:65–94, 1956). We consider a logistic-type production function, which comes from combining a Cobb–Douglas function and a linear pollution effect caused by increasing concentrations of capital. The difference between the production function and the classical logistic map comes from the presence of a parameter γ∈(0,1) in the exponent of one factor. We call this new function the gamma-logistic map. Our main purpose is to obtain sharp global stability conditions for the positive equilibrium of the model and to study how the stability properties of such equilibrium depend on the relevant model parameters. This study is developed by using some properties of the gamma-logistic map and some well-known results connecting stability in delay differential equations and discrete dynamical systems. Finally, we also compare the obtained results with the ones written in related articlesThis research has been partially supported by Ministerio de Educación, Cultura y Deporte of Spain (grant number FPU16/04416), Consellería de Cultura, Educación e Ordenación Universitaria da Xunta de Galicia (grant numbers ED481A-2017/030, GRC2015/004 and R2016/022) and Agencia Estatal de Investigación of Spain (grant number MTM2016-75140-P, cofunded by European Community fund FEDER)S

Global attraction in a system of delay differential equations via compact and convex sets

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems Series B following peer review. The definitive publisher-authenticated version [S. Buedo-Fernández. Global attraction in a system of delay differential equations via compact and convex sets, Discrete Contin Dyn. Syst., Ser. B 25 (2020), 3171-3181] is available online at: [https://www.aimsciences.org/article/doi/10.3934/dcdsb.2020056]We provide sufficient conditions for a concrete type of systems of delay differential equations (DDEs) to have a global attractor. The principal idea is based on a particular type of global attraction in difference equations in terms of nested, convex and compact sets. We prove that the solutions of the system of DDEs inherit the convergence to the equilibrium from an associated discrete dynamical systemThis research has been partially supported by funds initially conceded by Ministerio de Educación, Cultura y Deporte of Spain (grant number FPU16/04416) and by Consellería de Cultura, Educación e Ordenación Universitaria da Xunta de Galicia (grant number ED481A-2017/030). As part of a research group, the author also acknowledges funding from Xunta de Galicia (GRC2015/004, R2016/022 and ED431C 2019/02) and Agencia Estatal de Investigación of Spain (grant number MTM2016-75140-P, cofunded by European Community fund FEDER)S

Qualitative analysis of some models of delay differential equations

This thesis concerns the study of the global dynamics of delay differential equations of the so-called production and destruction type, which find applications to the modelling of several phenomena in areas such as population growth dynamics, economics, cell production, etc. For instance, by applying tools coming from discrete dynamics, we provide sufficient conditions for the existence of globally attracting equilibria for families of scalar or multidimensional equations. Moreover, we extend some known results in the scalar non-autonomous case by the use of integral inequalities. Finally, the existence of periodic solutions is analysed in the general context of infinite delay, impulses and periodic coefficients

Evaluation of Photosynthetic Capacity and Grain Yield of the Sea Level Quinoa Variety Titicaca Grown in a Highland Region of Northwest Argentine

Photosynthetic characterization of the quinoa cultivar Titicaca grown at the Encalilla site (1995m asl), a high mountain valley of the Argentinean Northwest, is described in this study. Titicaca cultivar,bred in Denmark from Chilean and Peruvian parenteral lines, is a promising short cycle cultivar anddaylength neutral photoperiod. Results showed that maximal photosynthetic CO2 assimilation (Amax)and stomatal conductance (gs) were similar to other quinoa varieties. However, carboxilation capacityand leaf transpiration (E) were significantly higher in Titicaca cultivar compared with other quinoacultivars grown in the same place. Assimilation of CO2 and stomatal conductance exhibited a strongcorrelation, like that occurs between (E) and (gs). Light saturation point (LSP) and light compensationpoint (LCP) were higher in relation to other quinoa cultivars. Grain yield of 2.35 and 2.51 g/plant wasrecorded and indicating a well adaptation to arid climatic conditions of the Argentinean Northwestregion. The highest value of UV protective pigments found in Titicaca will be explained by solarirradiance in the grown area in relation to Denmark conditions. Grain yield, harvest index and somephysiological parameters suggested a good adaptation of the Titicaca quinoa cultivar to high mountainvalleys of the Argentina Northwest. This means that Titicaca may be considered as a good alternativefor farmers in order to get similar production in less time.Fil: Gonzalez, Juan Antonio. Fundación Miguel Lillo; ArgentinaFil: Jacobsen, Sven E.. Universidad de Copenhagen; DinamarcaFil: Buedo, Sebastián Edgardo. Fundación Miguel Lillo; ArgentinaFil: Buedo, Sebastián Edgardo. Instituto Nacional de Tecnología Agropecuaria. Centro Regional Tucuman-Santiago del Estero. Estación Experimental Agropecuaria Famaillá; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Gonzalez, Daniela Alejandra. Universidad Nacional de Tucumán. Instituto de Bioprospección y Fisiología Vegetal. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet Noa Sur. Instituto de Bioprospección y Fisiología Vegetal; Argentin

Positive periodic solutions for impulsive differential equations with infinite delay and applications to integro‐differential equations

This is the accepted version of the following article: Buedo‐Fernández, S, Faria, T. Positive periodic solutions for impulsive differential equations with infinite delay and applications to integro‐differential equations. Math Meth Appl Sci. 2020; 43: 3052–3075, which has been published in final form at https://doi.org/10.1002/mma.6100. This article may be used for non-commercial purposes in accordance with the Wiley Self-Archiving Policy http://www.wileyauthors.com/self-archivingSufficient conditions for the existence of at least one positive periodic solution are established for a family of scalar periodic differential equations with infinite delay and nonlinear impulses. Our criteria, obtained by applying a fixed‐point argument to an original operator constructed here, allow to treat equations incorporating a rather general nonlinearity and impulses whose signs may vary. Applications to some classes of Volterra integro‐differential equations with unbounded or periodic delay and nonlinear impulses are given, extending and improving results in the literature.This work was supported by Ministerio de Educacion, Cultura y Deporte (Spain) under grant FPU16/04416 (Sebastián Buedo-Fernández) and by Fundação para a Ciência e a Tecnologia (Portugal) under project UID/MAT/04561/2019 (Teresa Faria)S

A new formula to get sharp global stability criteria for one-dimensional discrete-time models

This is a post-peer-review, pre-copyedit version of an article published in Qualitative Theory of Dynamical Systems. The final authenticated version is available online at: https://doi.org/10.1007/s12346-018-00314-4We present a new formula that makes it possible to get sharp global stability results for one-dimensional discrete-time models in an easy way. In particular, it allows to show that the local asymptotic stability of a positive equilibrium implies its global asymptotic stability for a new family of difference equations that finds many applications in population dynamics, economic models, and also in physiological processes governed by delay differential equations. The main ingredients to prove our results are the Schwarzian derivative and some dominance argumentsThe research of Sebastián Buedo-Fernández has been partially supported by Ministerio de Educación, Cultura y Deporte of Spain (Grant No. FPU16/04416), Consellería de Cultura, Educación e Ordenación Universitaria, Xunta de Galicia (Grant Nos. GRC2015/004 and R2016/022), and Agencia Estatal de Investigación of Spain (Grant MTM2016-75140-P, cofunded by European Community fund FEDER)S

Basic control theory for linear fractional differential equations with constant coefficients

In this paper we present an analogous result of the famous Kalman controllability criterion for first order linear ordinary differential equations with constant coefficients that applies to the case of linear differential equations of fractional order with constant coefficients. We use the fractional Gramian matrix, the range space and the Kalman matrix as main tools to derive a sufficient and necessary condition for the controllability of the fractional system. Moreover, we provide some simple examples, including a linear fractional harmonic oscillator, to illustrate our results. Finally, several open problems arising from this topic are suggested, including another simple linear system of incommensurate fractional ordersThis research has been partially supported by the AEI of Spain under Grant MTM2016-75140-P, co-financed by European Community fund FEDER and XUNTA de Galicia under grant ED431C 2019/02. Sebastián Buedo-Fernández also acknowledges current funding from Ministerio de Educación, Cultura y Deporte of Spain (FPU16/04416) and previous funding from Xunta de Galicia (ED481A-2017/030)S

On the stability properties of a delay differential neoclassical model of economic growth

The main aim of this paper is to establish sharp global stability conditions for the positive equilibrium of a well-known model of economic growth when a delay is considered in the production function. In order to deal with a broad scenario, we establish some results of global attraction for a general family of differential equations with variable delay; for it, we use the notion of strong attractor, which allows us to simplify the proofs, as well as to generalize previous results. Our study reveals that sometimes production delays are not able to destabilize the positive equilibrium, even if they are large. In other cases, the stability properties of the equilibrium depend on the interaction between the delay and other relevant model parameters, leading sometimes to stability windows in the bifurcation diagram

Gronwall-Bellman estimates for linear Volterra-type inequalities with delay

We obtain some estimates of Gronwall–Bellman-type for Volterra’s inequalities, which have applications to the study of the stability properties of the solutions to some linear functional differential equations

Gronwall–Bellman estimates for linear Volterra-type inequalities with delay

We obtain some estimates of Gronwall–Bellman-type for Volterra’s inequalities, which have applications to the study of the stability properties of the solutions to some linear functional differential equations