On non-uniqueness of cycles in 3D models of circular gene networks

V. P. Golubyatnikov

Čelâbinskij fiziko-matematičeskij žurnal, Tome 9 (2024) no. 1, pp. 23-34.

Résumé

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.

Détail

Keywords: gene network models, phase portraits of non-linear dynamical systems, equilibrium points, invariant domains, step functions, periodic trajectories.

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