Geodesic
On non-uniqueness of cycles in 3D models of circular gene networks
Čelâbinskij fiziko-matematičeskij žurnal, Tome 9 (2024) no. 1, pp. 23-34

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We describe 3-dimensional dynamical systems with piecewise linear right hand sides which simulate functioning of simplest molecualr repressilators and contain infinite one-parametric families of cycles in their phase portraits. An analogous dynamical system with step functions in its right hand sides is constructed; its phase portrait contains two piecewise linear cycles. A surface separating these two cycles is described.
Keywords: gene network models, phase portraits of non-linear dynamical systems, equilibrium points, invariant domains, step functions, periodic trajectories. 
@article{CHFMJ_2024_9_1_a1,
     author = {V. P. Golubyatnikov},
     title = {On non-uniqueness of cycles in {3D} models of circular gene networks},
     journal = {\v{C}el\^abinskij fiziko-matemati\v{c}eskij \v{z}urnal},
     pages = {23--34},
     publisher = {mathdoc},
     volume = {9},
     number = {1},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/CHFMJ_2024_9_1_a1/}
}
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V. P. Golubyatnikov. On non-uniqueness of cycles in 3D models of circular gene networks. Čelâbinskij fiziko-matematičeskij žurnal, Tome 9 (2024) no. 1, pp. 23-34. http://geodesic.mathdoc.fr/item/CHFMJ_2024_9_1_a1/