2023
On a dynamical model of happiness
(with Sergei Trofimchuk),
Math. Model. Nat. Phenon.18 (2023), No. 10 (15 pp.).
The peak-end rule and its dynamic realization through differential equations with maxima
(with Elena Trofimchuk and Sergei Trofimchuk),
Nonlinearity 36 (2023), 507-536.
2022
Stability, bifurcations and hydra effects in a stage-structured population
model with threshold harvesting (with Elisa Sovrano),
Communications in Nonlinear Science and Numerical Simulation 109 (2022), 106280 (1-15).
Bifurcation analysis of a piecewise smooth Ricker map with proportional
threshold harvesting, Journal of Difference Equations and Applications 28 (2022), 1268-1281.
2021
Destabilization and chaos induced by harvesting: Insights from one-dimensional discrete-time models (with V. Jiménez López), Journal of Mathematical Biology 82:3 (2021), 1-28.
2020
Clark's equation: a useful difference equation for population models, predictive control, and numerical approximations, Qualitative Theory of Dynamical Systems 19:71 (2020), 11pp.
Dynamics and bifurcations of a family of piecewise smooth maps arising in population models with threshold harvesting (con C. Lois-Prados), Chaos 30 (2020), 073108, 17 pp.
Threshold harvesting as a conservation or exploitation strategy in population management (with F. Hilker), Theoretical Ecology 13 (2020), 519-536.
A note on the Lasota discrete model for blood cell production (with C. Lois-Prados), Discrete and
Continuous Dynamical Systems, Series B 25 (2020), 701-713.
2019
Proportional threshold harvesting in discrete-time population models (with F. Hilker), Journal of Mathematical Biology 79 (2019), 1927-1951. Global asymptotic stability of a generalization of the Pielou difference equation (with Á. Garab y V. Jiménez López), Mediterranean Journal of Mathematics 16:93 (2019), 1-18.
A new formula to get sharp global stability criteria for one-dimensional discrete-time models (with S. Buedo Fernández), Qualitative Theory of Dynamical Systems 18 (2019), 813-824.
Some lessons from two simple approaches to model the impact of harvest timing on seasonal populations, A. Korobeinikov et al. (eds.), CRM Extended Abstracts Spring 2018, Trends in Mathematics 11,
Springer-Birkhauser, Basel, 2019, pp. 99-106.
2018
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.
2017
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.
2016
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. 2015
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. 2014
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. 2013
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).
2012
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.
2011
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.
2010
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.
2009
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
2008
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.
2007
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.
2006
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.
2005
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. 2004
Four theorems and one conjecture on the global asymptotic stability of delay
differential equations,
"The first 60 years of Nonlinear Analysis of Jean Mawhin" (M. Delgado et al., Eds.), pp. 117--129, World Scientific Publishing (2004). 2003
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),
1057-1073. Discrete Halanay-type inequalities and applications (with A. Ivanov y J. B.
Ferreiro), Nonlinear Analysis. Theory, Methods and Applications, Vol. 55 (2003), 669-678. 2002
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),
875-896
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.