Genetic engineering – construction of a network of arbitrary dimension with periodic attractor

Samuilik, Inna; Sadyrbaev, Felix

doi:10.21595/vp.2022.22992

Cited by 2 publications

(2 citation statements)

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“…The main approaches to the description of gene networks and modeling their dynamics are a logical description; a description of the gene network using a system of nonlinear differential equations [3]; stochastic gene network models; graph theory [1], Boolean modeling [1]. Nonlinear ordinary differential equations are the most-widespread formalism for modeling genetic regulatory networks [4][5][6][7].…”

Section: Introductionmentioning

confidence: 99%

Comparative Analysis of Models of Gene and Neural Networks

2023

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In the language of mathematics, the method of cognition of the surrounding world in which the description of the object is carried out the name is mathematical modeling. The study of the model is carried out using certain mathematical methods. The systems of the ordinary differential equations modeling artificial neuronal networks and the systems modeling the gene regulatory networks are considered. The one system consists of a sigmoidal function which depends on linear combinations of the arguments minus the linear part. The other system consists of a sigmoidal function which depends on the hyperbolic tangent function. The linear combinations and hyperbolic tangent functions of the arguments are described by one regulatory matrix. For the three-dimensional cases, two types of matrices are considered and the behavior of the solutions of the system is analyzed. The attracting sets are constructed for several cases. Illustrative examples are provided. The list of references consists of 19 items.

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Section: Introductionmentioning

confidence: 99%

Comparative Analysis of Models of Gene and Neural Networks

2023

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“…Limit cycles can emerge from stable focuses as a result of Andronov -Hopf bifurcation. Attractors were constructed in systems with dimensions higher than three [6], [7]. These attractors are not solutions themselves, but they attract periodic solutions of a system.…”

Section: Introductionmentioning

confidence: 99%