Attraction in n ‐dimensional differential systems from network regulation theory

19th International Scientific Conference Engineering for Rural Development Proceedings

2020

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We consider systems of two ordinary differential equations, which describe two-component Genomic Networks (GRN) and VNT (Virtual Network Topology) -controlled two dimensional telecommunication networks. VNT control over network is based on attractor selection like in biological (genomic) networks. We show that besides a set of stable critical points an attractor can be in the form of a stable periodic regime. We show the mechanism of emergence of a limit cycle through the Andronov-Hopf bifurcation. Similar attractors can appear in mathematical models with no limitations on dimensionality.

Section: Introductionmentioning

confidence: 83%

On modelling of artificial networks arising in applications

Atslega

19th International Scientific Conference Engineering for Rural Development Proceedings

2020

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“…We examine the behaviour of solutions and show that two of periodic solutions are stable limit cycles, which attract almost all the trajectories in G. We show what happens if the regulatory matrix changes its structure and the system (1) becomes coupled. Our study has connections with papers [9][10][11][12], where similar problems were studied. The novelty of the current paper is showing how periodic solutions can appear in 3D system and what are the conditions for their existence.…”

Section: Introductionmentioning

confidence: 85%

On modelling of complex networks

Atslega

20th International Scientific Conference Engineering for Rural Development Proceedings

Samuilik

2021

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A network is considered, which is modelled by a system of ordinary differential equations. The dynamics of a network depends on the attracting sets in a phase space. The problem of control and management of this network is in a focus of our study. The specific case is considered, where attractors are periodic trajectories. We provide the way of controlling the network by changing of a certain group of parameters. The numerical approach combined with the analytical solutions is used. As a by-product, the existence of multiple periodic solutions is proved. They are constructed explicitly for a specific three-dimensional system. Problems of control and management of systems of this kind are challenging issues in the theory of genetic networks.

“…More on two-dimensional systems can be found in [11], [12], [13], [15]. Extension of [11] to the n-dimensional case is in [14]. To be able for one to repeat the numerical experiments above, other parameters should be known.…”

Section: Two-element Grnmentioning

confidence: 99%

On Modelling of Genetic Regulatory Net Works

Wseas Transactions on Electronics

Samuilik

Sengileyev

2021

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We consider mathematical model of genetic regulatory networks (GRN). This model consists of a nonlinear system of ordinary differential equations. The vector of solutions X(t) is interpreted as a current state of a network for a given value of time t: Evolution of a network and future states depend heavily on attractors of system of ODE. We discuss this issue for low dimensional networks and show how the results can be applied for the study of large size networks. Examples and visualizations are provided