Bifurcation analysis of the statics and dynamics of a logistic model with two delays

TL;DR

This paper analyzes a discrete dynamical logistic model with two delays, deriving characteristic equations and illustrating bifurcation behavior through numerical examples like boundary bifurcation curves and Feigenbaum diagrams.

Contribution

It provides a detailed bifurcation analysis of a logistic model with two delays, including derivation of characteristic equations for various cycles and numerical illustrations.

Findings

Identification of boundary bifurcation curves

Feigenbaum diagrams illustrating complex dynamics

Characterization of system behavior with two delays

Abstract

The mathematical - numerical analysis of a discrete dynamical model with two independent delays was performed. Such model may describe a continuous system with delays that have real rational number values. Applicable characteristic equations were derived for both a single and double cycle. The results of the analysis were illustrated by numerical examples in the form of boundary bifurcation curves and Feigenbaums diagrams.