Research papers since 2002
(Updated January 16, 2019)
- Global asymptotic stability of a generalization of the Pielou difference equation (with Á. Garab and V. Jiménez López), accepted for publication in Mediterranean Journal of Mathematics.
- A new formula to get sharp global stability criteria for one-dimensional discrete-time models (with S. Buedo Fernández), Qualitative Theory of Dynamical Systems, published online, DOI: 10.1007/s12346-018-00314-4.
- Some lessons from two simple approaches to model the impact of harvest timing on seasonal populations, Trends in Mathematics: Research Perspectives CRM Barcelona, Summer 2018,
Springer-Birkhauser, Basel (the volume is to appear in 2019).
- On the stability properties of a delay differential neoclassical model of economic growth (with S. Buedo Fernández), Electron. J. Qual. Theory Differ. Equ. 43 (2018), 1-14.
- A new flexible discrete-time model for stable populations, Discrete and
Continuous Dynamical Systems, Series B 23 (2018), 2487-2498
- A global picture of the gamma-Ricker map: a flexible discrete-time model with factors of positive and negative density dependence, Bulletin of Mathematical Biology 80 (2018), 417-434.
- The Sixteenth Bellman Prize, Announcement in Mathematical Biosciences 294 (2017), I-II.
- Effects of strength and timing of harvest on seasonal population models: stability switches and catastrophic shifts, Theoretical Ecology 10 (2017), 235-244.
- On the global stability of periodic Ricker maps, Electron. J. Qual. Theory Differ. Equ. 76 (2016), 1-8.
- Potential impact of carry-over effects in the dynamics and management of seasonal populations (with A. Ruiz-Herrera), PLoS One 11 (2016), e0155579.
- Global dynamics of delay equations for populations with competition among immature individuals (with A. Ruiz-Herrera), Journal of Differential Equations, Vol. 260 (2016), 5926-5955.
- Endemic bubbles generated by delayed behavioral response: global stability and bifurcation switches in an SIS model (con M. Liu y G. Rost), SIAM Journal on Applied Mathematics, Vol. 75 (2015), 75-91.
- Delayed population models with Allee effects and exploitation (with A. Ruiz-Herrera), Mathematical Biosciences and Engineering, Vol. 12 (2015), 83-97.
- Harvesting and dynamics in some one-dimensional population models (with F. Hilker), in "Theory and Applications of Difference Equations and Discrete Dynamical Systems", Z. AlSharawi, J.M. Cushing, S. Elaydi (Eds.), Springer Proceedings in Mathematics & Statistics, Vol. 102 (2014), pp. 61-74.
- Addendum to "Attractivity, multistability, and bifurcation in delayed Hopfield's model with non-monotonic feedback" [J. Differential Equations 255 (11) (2013) 4244-4266]
(with A. Ruiz Herrera), Journal of Differential Equations, Vol. 257 (2014), 1307-1309.
- Delayed logistic population models revisited, Publicacions Matemàtiques, Vol. Extra (2014), 309-331.
- PBC-based pulse stabilization of periodic orbits (with C. Pötzsche), Physica D, Vol. 272 (2014), 26-38.
- Global dynamics of discrete neural networks allowing
non-monotonic activation functions (with A. Ruiz Herrera), Nonlinearity, Vol. 27 (2014), 289-304.
- Harvest timing and its population dynamic consequences in a discrete single-species model (with B. Cid y F. Hilker), Mathematical Biosciences, Vol. 248 (2014), 78-87.
- Attractivity, multistability, and bifurcation in delayed Hopfield's model with non-monotonic feedback (with A. Ruiz-Herrera), Journal of Differential Equations, Vol. 255 (2013), 4244-4266
- Global dynamics in a commodity market model (with
G. Rost), Journal of Mathematical Analysis and
Applications, Vol. 398 (2013), 707-714.
- Harvesting, census timing and "hidden'' hydra effects (with F. Hilker), Ecological Complexity, Vol. 14 (2013), 95-107.
- Prediction-based control of chaos and a dynamic Parrondo's paradox (with M. P. Fernández de Córdoba), Physics Letters A, Vol. 377 (2013), 778-782.
- A two-parameter method for chaos control and targeting in one-dimensional maps (with D. Franco), International Journal of Bifurcation and Chaos, Vol. 23 (2013), 1350003 (11 pages).
- Chaos in discrete structured population models (with A. Ruiz-Herrera), SIAM Journal on Applied Dynamical Systems, Vol. 11 (2012), 1200-1214.
- The hydra effect, bubbles, and chaos in a simple discrete population model with constant effort harvesting (with A. Ruiz-Herrera), Journal of Mathematical Biology, Vol. 65 (2012), 997-1016.
- On stabilization of equilibria using predictive control with and without pulses (with E. Braverman), Computers and Mathematics with Applications, Vol. 64 (2012), 2192-2201.
- Global dynamics in a stage-structured discrete-time population model with harvesting (with P. Pilarczyk), Journal of Theoretical Biology, Vol. 297 (2012), 148-165.
- Global stabilization of periodic orbits using a proportional feedback control with pulses (with E. Braverman), Nonlinear Dynamics, Vol. 67 (2012), 2467-2475.
- Bubbles for a class of delay differential equations (with
T. Krisztin), Qualitative Theory of Dynamical Systems, Vol. 10 (2011), 169-196.
- Stability of nonautonomous difference equations: simple ideas leading to useful results, Journal of Difference Equations and Applications, Vol. 17 (2011), 203-220.
- Global behaviour of a second order nonlinear difference equation (with I. Bajo), Journal of Difference Equations and Applications, Vol. 17 (2011), 1471-1486.
- Dichotomy results for delay
differential equations with negative Schwarzian derivative (with
G. Rost), Nonlinear Analysis: Real World Applications, Vol. 11 (2010), 1422-1430.
- Global stabilization of fixed points using predictive control (with D. Franco), Chaos, Vol. 20 (2010), 023124, 9 pp.
- Complex dynamics of survival and extinction in simple population models with harvesting, Theoretical Ecology, Vol. 3 (2010), 209-221.
- How to control chaotic behaviour and population size with proportional feedback, Physics Letters A, Vol. 374 (2010), 725-728.
- On the global attractor of delay differential equations with unimodal feedback (with
G. Rost), Discrete and
Continuous Dynamical Systems, Vol. 24 (2009), 1215-1224.
Global stability and bifurcations in a delayed discrete population model, Int. Journal of Qualitative Theory of Differential Equations and Applications, Vol. 3 (2009), 66-80
- Periodic points and stability in Clark's delayed recruitment model (with H. A. El-Morshedy y V. Jiménez López),
Nonlinear Analysis: Real World Applications, Vol. 9 (2008), 776-790. This pdf file includes a corrigendum published in Nonlinear Anal. Real World Appl., Vol. 10 (2009), 563.
- Local stability implies global stability in some one-dimensional discrete single-species models, Discrete and
Continuous Dynamical Systems, Series B, Vol. 7 (2007), 191-199.
- A sharp global stability result for a discrete population model, Journal of Mathematical Analysis and Applications, Vol. 330 (2007), 740-743.
- Existence of periodic solutions for functional equations with periodic delay (with D. Franco and P. Torres), Indian Journal of Pure and Applied Mathematics, Vol. 38 (2007), 143-152.
- Global stability in discrete population models with delayed-density dependence (with V. Tkachenko y S. Trofimchuk), Mathematical Biosciences, Vol. 199 (2006), 26-37.
- Globally attracting fixed points in higher order discrete population models (with H. A. El-Morshedy), Journal of Mathematical Biology, Vol. 53 (2006), 365-384.
- Periodicity on discrete dynamical systems generated by a class of rational mappings (with I. Bajo), Journal of Difference Equations and Applications, Vol. 12 (2006), 1201-1212.
- Exponential stability in a scalar functional differential equation (with M. Pituk), Journal of Inequalities and Applications, Art. 37195 (2006), 1-10.
- A global stability criterion for a family of delayed population models (with
V. Tkachenko y S. Trofimchuk), Quarterly of Applied Mathematics, Vol. 63 (2005), 56-70.
- On a generalized Yorke condition for scalar delayed population models (with T.
Faria, J.J. Oliveira y S. Trofimchuk), Discrete and
Continuous Dynamical Systems, Vol. 12 (2005), 481-500
- On explicit conditions for the asymptotic stability of linear higher order difference equations, Journal of Mathematical Analysis and Applications, Vol. 303 (2005), 492-498.
- Asymptotic estimates and exponential stability for higher order monotone difference equations (with
M. Pituk), Advances in Difference Equations, Vol. 2005, 41-55.
- Sufficient conditions for the global exponential stability of nonautonomous higher order difference equations (with L. Berezansky y E. Braverman), Journal of Difference Equations and Applications, Vol. 11 (2005), 785-798.
- Convergence to equilibria in discrete population models (with H. A. El-Morshedy), Journal of Difference Equations and Applications, Vol. 11 (2005), 117-131.
- Four theorems and one conjecture on the global asymptotic stability of delay
"The first 60 years of Nonlinear Analysis of Jean Mawhin" (M. Delgado et al., Eds.), pp. 117--129, World Scientific Publishing (2004).
- Wright type delay differential equations with negative Schwarzian (with M. Pinto, G. Robledo, V. Tkachenko y S. Trofimchuk) Discrete and
Continuous Dynamical Systems, Vol. 9 (2003), 309-321.
- A global stability criterion for scalar functional differential equations (with V.
Tkachenko y S. Trofimchuk),
SIAM Journal on Mathematical Analysis, Vol. 35 (2003), 596-622.
- Yorke and Wright 3/2-stability
theorems from a unified point of view (with V.
Tkachenko y S. Trofimchuk), Discrete and Continuous Dynamical Systems, Expanded
Vol. (2003), 580-589
- Global stability of a class of scalar nonlinear delay differential equations (with
A. Ivanov y S. Trofimchuk), Differential Equations and Dynamical Systems, Vol. 11 (2003), 33-54
- Boundedness and Asymptotic Stability for Delayed Equations of Logistic Type (with
T. Faria), Proceedings of the Royal Society of Edinburgh: Section A, Vol. 133 (2003),
- Discrete Halanay-type inequalities and applications (with A. Ivanov y J. B.
Ferreiro), Nonlinear Analysis. Theory, Methods and Applications, Vol. 55 (2003), 669-678.
- Halanay Inequality, Yorke 3/2 Stability Criterion and Differential Equations with
Maxima (with A. Ivanov y S. Trofimchuk),
Tohoku Mathematical Journal, Vol. 54 (2002), 277-295
- A note on the global stability of generalized difference equations (with J.B.
Ferreiro), Applied Mathematics Letters, Vol. 15 (2002), 655-659.
- Attractivity Properties of Infinite Delay Mackey-Glass type Equations (with C.
Martínez y S. Trofimchuk), Differential and Integral Equations, Vol. 15 (2002),
- Mackey-Glass type delay differential equations near the boundary of absolute
stability (with E. Trofimchuk y S. Trofimchuk), Journal of Mathematical Analysis and
Applications, Vol. 275 (2002), 747-760.