An investigation on the Lasota-Wazewska model with a piecewise constant argument

Abstract

This paper is devoted to investigating the asymptotic stability of the equilibrium point of the Lasota-Wazewska model with a piecewise constant argument and it is proved that this point is an attractor. It is also shown that every oscillatory solution of the corresponding difference equation has semi-cycles of length at least two.

On the Qualitative Behavior of the Difference Equation $\delta _{m+1}=\omega +\zeta \frac{f(\delta _{m},\delta _{m-1})}{\delta _{m-1}^{\beta}}$

“…At the same time, it can be said that the solution of even the simplest problem encountered in differential equations, which is another branch of applied mathematics, is more complex and more difficult than the difference equations. For this reason, difference equations have been used as an approach in the mathematical modelling of many physical, chemical and biological phenomena that can express with ordinary and partial differential equations (ODE and PDE) and in equations that are difficult to solve analytically [11].…”