• Publications
  • Influence
LOCAL STABILITY IMPLIES GLOBAL STABILITY IN SOME ONE-DIMENSIONAL DISCRETE SINGLE-SPECIES MODELS
We prove a criterion for the global stability of the positive equilibrium in discrete-time single-species population models of the form $x_{n+1}=x_nF(x_n)$. This allows us to demonstrate analyticallyExpand
  • 43
  • 6
  • PDF
A note on the global stability of generalized difference equations
In this note, we prove a discrete analogue of the continuous Halanay inequality and apply it to derive sufficient conditions for the global asymptotic stability of the equilibrium of certainExpand
  • 81
  • 5
  • PDF
A Global Stability Criterion for Scalar Functional Differential Equations
We consider scalar delay differential equations $x'(t) = -\delta x(t) + f(t,x_t) \ (*)$ with nonlinear f satisfying a sort of negative feedback condition combined with a boundedness condition. TheExpand
  • 69
  • 4
  • PDF
How to control chaotic behaviour and population size with proportional feedback
We study the control of chaos in one-dimensional discrete maps as they often occur in modelling population dynamics. For managing the population, we seek to suppress any possible chaotic behavior,Expand
  • 44
  • 3
  • PDF
Global dynamics in a stage-structured discrete-time population model with harvesting.
The purpose of this paper is to analyze the effect of constant effort harvesting upon global dynamics of a discrete-time population model with juvenile and adult stages. We consider differentExpand
  • 41
  • 3
  • PDF
Sufficient conditions for the global stability of nonautonomous higher order difference equations
We present some explicit sufficient conditions for the global stability of the zero solution in nonautonomous higher order difference equations. The linear case is discussed in detail. We illustrateExpand
  • 41
  • 3
  • PDF
Dichotomy results for delay differential equations with negative Schwarzian derivative
Abstract 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 theExpand
  • 34
  • 3
  • PDF
Existence and Stability of Almost Periodic Solutions for Quasilinear Delay Systems and the Halanay Inequality
We present some easily verifiable conditions for the existence and global asymptotical stability of almost periodic solutions to systems of delay differential equations in the form u′(t) = −Au(t) +Expand
  • 32
  • 3
Stability of non-autonomous difference equations: simple ideas leading to useful results
We address the stability properties in a non-autonomous difference equation where f is continuous, and the zero solution is assumed to be the unique equilibrium. We focus our discussion on twoExpand
  • 22
  • 3
  • PDF
Boundedness and asymptotic stability for delayed equations of logistic type
For a scalar Lotka–Volterra-type delay equation x ( t ) = b ( t ) x ( t )[1 − L ( x t )], where L : C ([− r , 0];R) → R is a bounded linear operator and b a positive continuous function, sufficientExpand
  • 8
  • 3
  • PDF