231 research outputs found
Delayed logistic population models revisited
We discuss the global dynamics of some logistic models governed by delay-differential equations. We focus on models of exploited populations, and study the changes in the dynamics as the harvesting effort is increased. We get new results and highlight the link among different logistic equations usually employed in population models
Delayed logistic population models revisited
We discuss the global dynamics of some logistic models governed by delay-differential equations. We focus on models of exploited populations, and study the changes in the dynamics as the harvesting effort is increased. We get new results and highlight the link among different logistic equations usually employed in population models
Sobre ecuaciones diferenciales con retraso, dinámica de poblaciones y números primos
Aprovecharemos para dar a conocer algunos aspectos de las ecuaciones con retraso y pasearemos por el mundo de los sistemas dinámicos discretos. Por el medio aparecen números mágicos y personajes inquietantes que ayudarán a hacer más amena la lectura
On explicit conditions for the asymptotic stability of linear higher order difference equations
AbstractWe derive some explicit sufficient conditions for the asymptotic stability of the zero solution in a general linear higher order difference equation, and compare our estimations with other related results in the literature. Our main result also applies to some nonlinear perturbations satisfying a kind of sublinearity condition
On stabilization of equilibria using predictive control with and without pulses
AbstractConsider a chaotic difference equation xn+1=f(xn). We focus on the problem of control of chaos using a prediction-based control (PBC) method. If f has a unique positive equilibrium, it is proved that global stabilization of this equilibrium can be achieved under mild assumptions on the map f; if f has several positive equilibria, we demonstrate that more than one equilibrium can be stabilized simultaneously. We also show that it is still possible to stabilize an unstable equilibrium using a strategy of control with pulses, that is, the control is only applied after a fixed number of iterations. We illustrate our main results with several examples, mainly from population dynamics
On the Global Attractor of Delay Differential Equations with Unimodal Feedback
We give bounds for the global attractor of the delay differential equation
, where is unimodal and has negative
Schwarzian derivative. If and satisfy certain condition, then,
regardless of the delay, all solutions enter the domain where f is monotone
decreasing and the powerful results for delayed monotone feedback can be
applied to describe the asymptotic behaviour of solutions. In this situation we
determine the sharpest interval that contains the global attractor for any
delay. In the absence of that condition, improving earlier results, we show
that if the d5A5Aelay is sufficiently small, then all solution enter the domain
where is negative. Our theorems then are illustrated by numerical examples
using Nicholson's blowflies equation and the Mackey-Glass equation.Comment: 10 pages, submitted to Discrete and Continuous Dynamical
Systems-Series A (DCDS
Mackey-Glass type delay differential equations near the boundary of absolute stability
For equations with -nonlinearity which has negative Schwarzian derivative and
satisfies for , we prove convergence of all solutions to
zero when both and are less than some constant
(independent on ). This result gives additional insight to the
conjecture about the equivalence between local and global asymptotical
stabilities in the Mackey-Glass type delay differential equations.Comment: 16 pages, 1 figure, accepted for publication in the Journal of
Mathematical Analysis and Application
Yorke and Wright 3/2-stability theorems from a unified point of view
We consider a family of scalar delay differential equations ,
with a nonlinearity satisfying a negative feedback condition combined with
a boundedness condition. We present a global stability criterion for this
family, which in particular unifies the celebrated 3/2-conditions given for the
Yorke and the Wright type equations. We illustrate our results with some
applications.Comment: 10 pages, accepted for publication in the Expanded Volume of DCDS,
devoted to the fourth international conference on Dynamical Systems and
Differential Equations, held at UNC at Wilmington, May 2002. Minor changes
from the previous versio
Dichotomy results for delay differential equations with negative Schwarzian
We gain further insight into the use of the Schwarzian derivative to obtain
new results for a family of functional differential equations including the
famous Wright's equation and the Mackey-Glass type delay differential
equations. We present some dichotomy results, which allow us to get easily
computable bounds of the global attractor. We also discuss related conjectures,
and formulate new open problems.Comment: 16 pages, submitted to Chaos,Solitons,Fractal
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