Topological-numerical analysis of global dynamics in the discrete-time two-gene Andrecut-Kauffman model
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914368187269120 |
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| author | Falęcki, Dorian Rosman, Mikołaj Palczewski, Michał Pilarczyk, Paweł Bartłomiejczyk, Agnieszka |
| author_facet | Falęcki, Dorian Rosman, Mikołaj Palczewski, Michał Pilarczyk, Paweł Bartłomiejczyk, Agnieszka |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_03850 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Topological-numerical analysis of global dynamics in the discrete-time two-gene Andrecut-Kauffman model Falęcki, Dorian Rosman, Mikołaj Palczewski, Michał Pilarczyk, Paweł Bartłomiejczyk, Agnieszka Dynamical Systems Primary: 37N25, 65P20, Secondary: 37D45, 37G35, 92C42 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. |
| title | Topological-numerical analysis of global dynamics in the discrete-time two-gene Andrecut-Kauffman model |
| topic | Dynamical Systems Primary: 37N25, 65P20, Secondary: 37D45, 37G35, 92C42 |
| url | https://arxiv.org/abs/2603.03850 |