Control and Harvesting in Discrete Population Models
A two-parameter method for chaos control and targeting in one-dimensional maps (with D. Franco), International Journal of Bifurcation and Chaos, in press.
On stabilization of equilibria using predictive control with and without pulses (with E. Braverman), Computers and Mathematics with Applications, published online, doi:10.1016/j.camwa.2012.01.013.
The hydra effect, bubbles, and chaos in a simple discrete population model with constant effort harvesting (with A. Ruiz-Herrera), Journal of Mathematical Biology, published online, doi:10.1007/s00285-011-0489-2.
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.
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.
Global stability of general difference equations
In the following papers, we have investigated the global stability of difference equations using different methods based on new discrete inequalities and monotonicity arguments. A note on the global stability of generalized difference equations (con J.B.
Ferreiro), Applied Mathematics Letters, Vol. 15 (2002), 655-659. Discrete Halanay-type inequalities and applications (con A. Ivanov y J. B.
Ferreiro), Nonlinear Analysis. Theory, Methods and Applications, Vol. 55 (2003), 669-678. 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 (con
M. Pituk), Advances in Difference Equations, Vol. 2005, 41-55. Sufficient conditions for the global exponential stability of nonautonomous higher order difference equations (con L. Berezansky y E. Braverman), Journal of Difference Equations and Applications, Vol. 11 (2005), 785-798. Stability of nonautonomous difference equations: simple ideas leading to useful results, Journal of Difference Equations and Applications, Vol. 17 (2011), 203-220. Stability and periodicity in discrete population models
Convergence to equilibria in discrete population models (with H. A. El-Morshedy), Journal of Difference Equations and Applications, Vol. 11 (2005), 117-131. Global stability in discrete population models with delayed-density dependence (with V. Tkachenko and 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.
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.
Periodic points and stability in Clark's delayed recruitment model (with H. A. El-Morshedy and 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.
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.
Rational Mappings
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.
Global behaviour of a second order nonlinear difference equation (with I. Bajo), Journal of Difference Equations and Applications, Vol. 17 (2011), 1471-1486.