# Projects / Mathematical Models of Gene Networks

This project aims to describe the mathematical model of various gene networks: build systems of differential equations that simulate biological systems; analyze corresponding dynamical systems; find stationary points, limit cycles, and bifurcations; develop software for numerical simulations. The latest work is dedicated to the central regulatory circuit of the morphogenesis system of D. Melanogaster.

I was working on this project with fellows from Sobolev Institute of Mathematics SB RAS and Institute of Cytology and Genetics SB RAS. It was also the primary research topic of my PhD thesis “Mathematical and numerical modeling of gene network artificial regulatory circuits.”

### Papers (25)

- Stratifications and foliations in phase portraits of gene network models (2023) by Andrey Akinshin et al.
- Mathematical and numerical modelling of the circadian oscillator (2022) by Andrey Akinshin et al.
- On a Numerical Model of a Circadian Oscillator (2022) by Andrey Akinshin et al.
- A Model of one central regulatory circuit (2020) by Andrey Akinshin et al.
- Mathematical and Numerical Models of the Central Regulatory Circuit of the Morphogenesis System... (2020) by Andrey Akinshin et al.
- On discrete structures in phase portraits of some non-linear dynamical systems (2016) by Andrey Akinshin et al.
- State transition diagrams in hypothetical models of cyclic gene networks functioning (2015) by Andrey Akinshin et al.
- A model of one biological 2-cells complex (2014) by Andrey Akinshin et al.
- Mathematical modeling of interaction of two cells in proneural cluster of D.mealnogaster (In Ru... (2014) by Andrey Akinshin et al.
- Symmetry in gene network models (2014) by Andrey Akinshin et al.
- Analysis of phase portraits in some gene networks models (2013) by Andrey Akinshin
- Mathematical and computational models of gene networks functioning (2013) by Andrey Akinshin et al.
- Numerical analysis of gene networks models (2013) by Andrey Akinshin
- Oscillating trajectories in some nonlinear dynamical systems (2013) by Andrey Akinshin et al.
- Computer analysis of phase portraits in gene networks models (2012) by Andrey Akinshin
- Geometric characteristics of cycles in some symmetric dynamical systems (In Russian) (2012) by Andrey Akinshin et al.
- On Nonuniqueness of Cycles in Dissipative Dynamical Systems of Chemical Kinetics (2012) by Andrey Akinshin et al.
- Research of discrete structures in some cyclic dynamical systems (In Russian) (2012) by Andrey Akinshin
- Mathematical and numerical modeling of gene network functioning (2011) by Andrey Akinshin et al.