Genetic engineering – construction of a network of four dimensions with a chaotic attractor

Samuilik, Inna

doi:10.21595/vp.2022.22829

Cited by 6 publications

(2 citation statements)

References 6 publications

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“…The Lyapunov exponent (LE) is one of the approaches to detect chaos [8]. We have (0; −; −; −), then the system (1) has periodic solutions [9]. Now consider b = 0.045…”

Section: Fig 1 Graph Corresponding To the System (1)mentioning

confidence: 99%

On mathematical models of artificial neural networks

Samuilik

Sadyrbaev

Atslega

2023

22nd International Scientific Conference Engineering for Rural Development Proceedings

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Artificial Neural Networks are in focus. The four-dimensional and the five-dimensional systems are considered. The activation function – hyperbolic tangent is used to model the Artificial Neural Networks. By changing one of the parameters in the system, different types of solutions are obtained: periodic solutions and chaotic solutions. The graphs of all solutions, the dynamics of Lyapunov exponents and 2D and 3D projections of attractors are provided using Wolfram Mathematica.

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“…The Lyapunov exponent (LE) is one of the approaches to detect chaos [8]. We have (0; −; −; −), then the system (1) has periodic solutions [9]. Now consider b = 0.045…”

Section: Fig 1 Graph Corresponding To the System (1)mentioning

confidence: 99%

On mathematical models of artificial neural networks

Samuilik

Sadyrbaev

Atslega

2023

22nd International Scientific Conference Engineering for Rural Development Proceedings

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“…In the system Eq. (1) the sigmoid logistic function 𝑓 𝑧 = is used [4]. It is to be mentioned, that first system of this form was used to model populations of neurons [5], [6].…”

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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Mathematical Modeling of Four-dimensional Genetic Regulatory Networks Using a Logistic Function

Samuilik¹

2022

Wseas Transactions on Computer Research

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Mathematical modeling is a universal tool for the study of complex systems. In this paper formulas for characteristic numbers of critical points for the systems of order four (4D) are considered. We show how an unstable focus-focus can appear in a four-dimensional system. Projections of 4D trajectories on two-dimensional and threedimensional subspaces are shown. In the considered four-dimensional system the logistic function is used. The research aims to investigate the four-dimensional system, find critical points of the system, calculate the characteristic numbers, and calculate Lyapunov exponents.

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Genetic engineering – construction of a network of four dimensions with a chaotic attractor

Cited by 6 publications

References 6 publications

On mathematical models of artificial neural networks

On mathematical models of artificial neural networks

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

Mathematical Modeling of Four-dimensional Genetic Regulatory Networks Using a Logistic Function

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