Abstract
We obtain conditions for uniqueness of a cycle in the phase portrait of a piecewise linear dynamical system of the Elowitz–Leibler type which simulates the functioning of a simplest circular gene network. We describe the behavior of trajectories of this system in the invariant toric neighborhood of the cycle.
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Acknowledgments
The authors are sincerely grateful to V.V. Ivanov and an anonymous referee for their useful advice and critical remarks.
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Translated from Sibirskii Matematicheskii Zhurnal, 2022, Vol. 63, No. 1, pp. 95–103. https://doi.org/10.33048/smzh.2022.63.106
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Golubyatnikov, V.P., Minushkina, L.S. On Uniqueness of a Cycle in One Circular Gene Network Model. Sib Math J 63, 79–86 (2022). https://doi.org/10.1134/S0037446622010062
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DOI: https://doi.org/10.1134/S0037446622010062
Keywords
- circular gene network
- positive and negative feedbacks
- block-linear dynamical system
- invariant domain
- Poincaré map
- fixed point
- cycle