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Abstract
We conduct numerical analysis of the 2-dimensional discrete-time gene expression model originally introduced by Andrecut and Kauffman (Phys. Lett. A 367: 281–287, 2007). In contrast to the previous studies, we analyze the dynamics with different reaction rates α1 and α2 for each of the two genes under consideration. We explore bifurcation diagrams for the model with α1 varying in a wide range and α2 fixed. We detect chaotic dynamics by means of the positive maximum Lyapunov exponent, and we scan through selected parameters to detect those combinations for which chaotic dynamics can be found in the model. Moreover, we find bistability in the model, that is, the existence of two disjoint attractors. Both situations are interesting from the point of view of applications, as they imply unpredictability of the dynamics encountered. Finally, we show some specific values of parameters of the model in which the two attractors are of different kind (a periodic orbit and a chaotic attractor) or of the same kind (two periodic orbits or two chaotic attractors).
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- Accepted or Published Version
- DOI:
- Digital Object Identifier (open in new tab) 10.34808/xre5-vy14
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
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DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
ISSN: 1531-3492 - Language:
- English
- Publication year:
- 2025
- Bibliographic description:
- Rosman M., Palczewski M., Pilarczyk P., Bartłomiejczyk A.: Bistability and chaos in the discrete two-gene Andrecut-Kauffman model// DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B -, (2025),
- DOI:
- Digital Object Identifier (open in new tab) 10.3934/dcdsb.2025028
- Sources of funding:
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- Project Topological and numerical methods in dynamical systems
- IDUB Technetium Technetium Talent Management Grants DEC-27/1/2022/IDUB/III.4c/Tc "Od teorii do zastosowań w modelowaniu matematycznym", kierownik projektu Agnieszka Bartłomiejczyk
- Verified by:
- Gdańsk University of Technology
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