Topological chaos in the two-gene Andrecut-Kauffman model

2025/09/15 by Jörg Neunhäuserer, Neunhäuserer, Jörg
Computer Science · #37B40 #37N25 #65P20 #92C42 #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation

paper · pdf · doi:10.48550/arxiv.2509.11881

openalex publication_date 2025/09/15 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28

Abstract

The two-gene Andrecut-Kauffman model describes gene expression within cells by a two-dimensional discrete dynamical system. Using periodic orbits of an one dimensional subsystem we, rigourously prove the existence of topological chaos in this system. In addition we compute parameter domains of the system where we have topological chaos.

Citations

• Justification of quasi-stationary approximation in models of gene expression of a self-regulating protein
• Sets of “Non-typical” points have full topological entropy and full Hausdorff dimension
• Topological entropy for noncompact sets

Related

• Topological–numerical analysis of global dynamics in the discrete-time two-gene Andrecut–Kauffman model
• Bistability and chaos in the discrete two-gene Andrecut-Kauffman model
• Modular Gene Dynamics and Network Theory at Mesoscopic Scale
• Hamiltonian dynamics and distributed chaos in DNA
• Topological-numerical analysis of a two-dimensional discrete neuron model