Modelling Three Dimensional Gene Regulatory Networks

Samuilik, Inna; Sadyrbaev, Felix

doi:10.37394/23203.2021.16.67

Cited by 6 publications

(7 citation statements)

References 18 publications

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“…For this, the analysis of the phase space is needed. Future states are heavily dependent on attractors of the system, [4], [5]. In this note we will show that the three-dimensional system of the form Eq.…”

Section: Introductionmentioning

confidence: 92%

On a three-dimensional neural network model

Ogorelova¹,

Sadyrbaev²

2022

Vib. proced.

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Section: Introductionmentioning

confidence: 92%

On a three-dimensional neural network model

Ogorelova¹,

Sadyrbaev²

2022

Vib. proced.

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“…The dynamics of Lyapunov exponents (LE 1 = 0.03, LE 2 = 0; LE 3 = -1.16) are shown in Figure 8. At the end of the 70s of the last century, the Kaplan-Yorke formula was proposed to estimate the fractal size-in terms of Lyapunov exponents [12].…”

Section: An Example Of the System (2) With A Chaotic Solutionmentioning

confidence: 99%

“…Similar to a natural analog, an artificial neural network consists of neurons and synapses [9]. Neural networks are used to solve many problems: recognition and generation of images (face identification in video surveillance systems); speech and language (language for chat-bots and service robots); weather prediction; medical diagnosis [9][10]; business fields [11][12]; traffic monitoring systems [13].…”

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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“…where 𝜇 0, 𝜃 and 𝑣 0 are parameters, and 𝑤 are elements of the 𝑛 𝑛 regulatory matrix 𝑊. The parameters of the GRN have the biological interpretations [2,3].…”

Section: Introductionmentioning

confidence: 99%

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

Samuilik¹,

Sadyrbaev²

2022

Vib. proced.

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It is shown, how to construct a system of ordinary differential equations of arbitrary order, which has the periodic attractor and models some genetic network of arbitrary size. The construction is carried out by combining of multiple systems of lower dimensions with known periodic attractors. In our example the six-dimensional system is constructed, using two identical three-dimensional systems, which have stable periodic solutions.

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Modelling Three Dimensional Gene Regulatory Networks

Cited by 6 publications

References 18 publications

On a three-dimensional neural network model

On a three-dimensional neural network model

Comparative Analysis of Models of Gene and Neural Networks

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

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