Topological-numerical analysis of global dynamics in the discrete-time two-gene Andrecut-Kauffman model

We conduct a topological-numerical analysis of global dynamics in a discrete-time two-gene Andrecut-Kauffman model. This model describes gene expression regulation through nonlinear interactions. We use rigorous numerical methods to construct Morse decomposition of the system across a wide range of parameters. We obtain qualitative results by effectively computing the Conley indices of the constructed isolating neighborhoods that form the Morse decomposition. We introduce new symbols to convey the information provided by the Conley index in an easy to understand schematic way. We additionally conduct numerical simulations aimed at confirming the presence of complex dynamical phenomena, including multistability and the existence of chaotic attractors. The results demonstrate the usefulness of topological methods in understanding the global structure of dynamics in a gene regulatory model and highlight the richness of dynamics that can be observed in such a system when parameter values change.

• Publication year

  2026

• Venue

  Unknown venue

• Publication date

  2026-03-04

• Fields of study

  Biology, Mathematics

• Identifiers
  arXiv 2603.03850
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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