Chaotic and non-chaotic mixed oscillations in a logistic systems with delay

TL;DR

This paper analyzes a logistic system with delay, revealing it can produce mixed oscillations that are partly chaotic and partly predictable, even without bifurcations, demonstrated through simple models and feedback reactors.

Contribution

It provides a theoretical analysis showing that delayed logistic systems can generate semi-chaotic oscillations without bifurcations, expanding understanding of complex dynamics.

Findings

Systems can produce semi-chaotic oscillations

Oscillations occur without dynamic bifurcations

Examples include simple logistic models and feedback reactors

Abstract

The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the solutions of the mathematical method are characterized by no dynamic bifurcations. It has also been shown that the time series of the state variables of such a system may behave in a semi-chaotic way. This means that they have then predictable and unpredictable fragments. The analysis has been illustrated by two examples, viz. of a simple logistic model and of a reactor with feedback.