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

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 numerical approximation using differential equations with piecewise-constant arguments

In this paper we give a brief overview of the application of delay differential equations with piecewise constant arguments (EPCAs) for obtaining numerical approximation of delay differential equations, and we show that this method can be used for numerical approximation in a class of age-dependent population models. We also formulate an open problem for a qualitative behaviour of a class of li...

On the Global Attractivity of a Max-Type Difference Equation

Modeling a Tumor Growth with Piecewise Constant Arguments

β 0 x(⟦t⟧) − β 1 x(⟦t − 1⟧)) + γ 1 x(⟦t⟧) + γ 2 x(⟦t − 1⟧)}, where the parameters α, β 0 , β 1 , and r denote positive numbers, γ 1 and γ 2 are negative numbers and ⟦t⟧ is the integer part of t ∈ [0,∞). Equation (A) explains a brain tumor growth, where γ 1 is embedded to show the drug effect on the tumor and γ 2 is a rate that causes a negative effect by the immune system on the tumor populatio...