On the global attractivity for a logistic equation with piecewise constant arguments*1

Global Attractivity and Oscillations in a Periodic Delay - Logistic Equation

in which r and K are positive numbers; r is related to the reproduction of the species while K is related to the capacity of the environment to sustain the population. It is assumed that there is no immigration or emigration and other characteristics such as age dependence and interactions with other species are assumed to be not significant. Elementary analysis of (1.1) indicates that the solu...

Global dynamics of a differential equation with piecewise constant argument

Several aspects of global dynamics are studied for the scalar differential-difference equation εẋ(t) + x(t) = f (x([t])), 0 < ε 1, where [·] is the integer part function. The equation is a particular case of the special discretization (discrete version) of the singularly perturbed differential delay equation εẋ(t)+ x(t) = f (x(t−1)). Sufficient conditions for the invariance, global stability of...

On the Global Attractivity of a Max-Type Difference Equation

Global Attractivity in a Nonlinear Difference Equation

In this paper, we study the asymptotic behavior of positive solutions of the nonlinear difference equation xn+1 = xnf(xn−k), where f : [0,∞)→ (0,∞) is a unimodal function, and k is a nonnegative integer. Sufficient conditions for the positive equilibrium to be a global attractor of all positive solutions are established. Our results can be applied to to some difference equations derived from ma...

On global attractivity of solutions of a functional-integral equation

We prove an existence theorem for a quadratic functional-integral equation of mixed type. The functional-integral equation studied below contains as special cases numerous integral equations encountered in nonlinear analysis. With help of a suitable measure of noncompactness, we show that the functional integral equation of mixed type has solutions being continuous and bounded on the interval [...