We concern the asymptotic behaviour of the dynamical systems induced by nonlinear Lasota equation. We study chaoticity in the sense of Devaney and strong stability of the system. In many articles authors consider the properties of the linear version of the equation. By the construction of the operator in the separable space, we can formulate the relations between the solutions of the linear equation and its nonlinear version in Lebesgue space. The aim of the paper is to present the detailed construction of the operator thanks to which, the study of simple relationships allows determining the chaotic behaviour of the nonlinear equation.

中文翻译：

---

Lebesgue空间中非线性Lasota方程的混沌行为

我们关注由非线性Lasota方程引起的动力学系统的渐近行为。我们从Devaney和系统的强大稳定性的角度研究混沌。在许多文章中，作者都​​考虑了方程的线性形式的性质。通过在可分离空间中构造算子，我们可以在Lebesgue空间中公式化线性方程的解与其非线性形式之间的关系。本文的目的是介绍算子的详细结构，由此，对简单关系的研究可以确定非线性方程的混沌行为。