# Piecewise Linear Dynamical System Modeling Gene Network with Variable Feedback

## Abstract

We construct a discretization of the phase portrait of a 3-dimensional dynamical system of biochemical kinetics with piecewise linear right-hand sides. We describe geometry of the phase portrait and construct an invariant piecewise linear surface bounded by a stable cycle of this system composed of eight linear segments.

- Authors:

- Sobolev Institute of Mathematics SB RAS (Russian Federation)
- I.I. Pozunov Altai State Technical University (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 22771406

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Mathematical Sciences

- Additional Journal Information:
- Journal Volume: 230; Journal Issue: 1; Other Information: Copyright (c) 2018 Springer Science+Business Media, LLC, part of Springer Nature; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 1072-3374

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICAL METHODS AND COMPUTING; COMPUTERIZED SIMULATION; DYNAMICAL SYSTEMS; GENES; GEOMETRY; KINETICS; SURFACES; THREE-DIMENSIONAL CALCULATIONS

### Citation Formats

```
Golubyatnikov, V. P., E-mail: glbtn@math.nsc.ru, and Kazantsev, M. V., E-mail: markynaz.astu@gmail.com.
```*Piecewise Linear Dynamical System Modeling Gene Network with Variable Feedback*. United States: N. p., 2018.
Web. doi:10.1007/S10958-018-3725-0.

```
Golubyatnikov, V. P., E-mail: glbtn@math.nsc.ru, & Kazantsev, M. V., E-mail: markynaz.astu@gmail.com.
```*Piecewise Linear Dynamical System Modeling Gene Network with Variable Feedback*. United States. doi:10.1007/S10958-018-3725-0.

```
Golubyatnikov, V. P., E-mail: glbtn@math.nsc.ru, and Kazantsev, M. V., E-mail: markynaz.astu@gmail.com. Sun .
"Piecewise Linear Dynamical System Modeling Gene Network with Variable Feedback". United States. doi:10.1007/S10958-018-3725-0.
```

```
@article{osti_22771406,
```

title = {Piecewise Linear Dynamical System Modeling Gene Network with Variable Feedback},

author = {Golubyatnikov, V. P., E-mail: glbtn@math.nsc.ru and Kazantsev, M. V., E-mail: markynaz.astu@gmail.com},

abstractNote = {We construct a discretization of the phase portrait of a 3-dimensional dynamical system of biochemical kinetics with piecewise linear right-hand sides. We describe geometry of the phase portrait and construct an invariant piecewise linear surface bounded by a stable cycle of this system composed of eight linear segments.},

doi = {10.1007/S10958-018-3725-0},

journal = {Journal of Mathematical Sciences},

issn = {1072-3374},

number = 1,

volume = 230,

place = {United States},

year = {2018},

month = {4}

}

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