Random periodic sequence of globally mean-square exponentially stable discrete-time stochastic genetic regulatory networks with discrete spatial diffusions

Bin Wang; Bin Wang

doi:10.3934/era.2023157

Electronic Research Archive

2023, Volume 31, Issue 6: 3097-3122. doi: 10.3934/era.2023157

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Research article

Random periodic sequence of globally mean-square exponentially stable discrete-time stochastic genetic regulatory networks with discrete spatial diffusions

Bin Wang ^,

Department of Mathematics, Minzu Normal University of Xingyi, Xingyi 562400, Guizhou, China

Academic Editor: Dejing Dou

Received: 08 February 2023 Revised: 07 March 2023 Accepted: 08 March 2023 Published: 23 March 2023

This paper regards the dual effects of discrete-space and discrete-time in stochastic genetic regulatory networks via exponential Euler difference and central finite difference. Firstly, the global exponential stability of such discrete networks is investigated by using discrete constant variation formulation. In particular, the optimal exponential convergence rate is explored by solving a nonlinear optimization problem under nonlinear constraints, and an implementable computer algorithm for computing the optimal exponential convergence rate is given. Secondly, random periodic sequence for such discrete networks is investigated based on the theory of semi-flow and metric dynamical systems. The researching findings show that the spatial diffusions with nonnegative intensive coefficients have no influence on global mean square boundedness and stability, random periodicity of the networks. This paper is pioneering in considering discrete spatial diffusions, which provides a research basis for future research on genetic regulatory networks.
- genetic regulatory,
- spatial diffusion,
- stochastic,
- random periodicity,
- optimal convergence rate
Citation: Bin Wang. Random periodic sequence of globally mean-square exponentially stable discrete-time stochastic genetic regulatory networks with discrete spatial diffusions[J]. Electronic Research Archive, 2023, 31(6): 3097-3122. doi: 10.3934/era.2023157

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Abstract

This paper regards the dual effects of discrete-space and discrete-time in stochastic genetic regulatory networks via exponential Euler difference and central finite difference. Firstly, the global exponential stability of such discrete networks is investigated by using discrete constant variation formulation. In particular, the optimal exponential convergence rate is explored by solving a nonlinear optimization problem under nonlinear constraints, and an implementable computer algorithm for computing the optimal exponential convergence rate is given. Secondly, random periodic sequence for such discrete networks is investigated based on the theory of semi-flow and metric dynamical systems. The researching findings show that the spatial diffusions with nonnegative intensive coefficients have no influence on global mean square boundedness and stability, random periodicity of the networks. This paper is pioneering in considering discrete spatial diffusions, which provides a research basis for future research on genetic regulatory networks.

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