Analysis of finite-time stability in genetic regulatory networks with interval time-varying delays and leakage delay effects

Nayika Samorn; Kanit Mukdasai; Issaraporn Khonchaiyaphum; Nayika Samorn; Kanit Mukdasai; Issaraporn Khonchaiyaphum

doi:10.3934/math.20241220

AIMS Mathematics

2024, Volume 9, Issue 9: 25028-25048. doi: 10.3934/math.20241220

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Research article

Analysis of finite-time stability in genetic regulatory networks with interval time-varying delays and leakage delay effects

1.
Faculty of Agriculture and Technology, Nakhon Phanom University, Nakhon Phanom 48000, Thailand
2.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
3.
Department of Mathematics, Faculty of Engineering, Rajamangala University of Technology Isan, Khon Kaen Campus, Khon Kaen 40000, Thailand

Received: 01 July 2024 Revised: 05 August 2024 Accepted: 16 August 2024 Published: 27 August 2024
MSC : 34K20, 93D05, 93D40, 34D20

We primarily examined the effect of leakage delays on finite-time stability problems for genetic regulatory networks with interval time-varying delays. Since leakage delays can occur within the negative feedback components of networks and significantly impact their dynamics, they may potentially cause instability or suboptimal performance. The derived criteria encompass both leakage delays and discrete interval time-varying delays through the construction of a Lyapunov-Krasovskii function. We employed the estimation of various integral inequalities and a reciprocally convex technique. Additionally, these models consider lower bounds on delays, which may be either positive or zero, and allow for the derivatives of delays to be either positive or negative. Consequently, new criteria for genetic regulatory networks with interval time-varying delays under the effect of leakage delays are expressed in the form of linear matrix inequalities. Ultimately, a numerical example is presented to show the effect of leakage delays and to emphasize the significance of our theoretical findings.
- finite-time stability,
- genetic regulatory networks,
- leakage delays,
- lyapunov-Krasovskii functional,
- interval time-varying delay
Citation: Nayika Samorn, Kanit Mukdasai, Issaraporn Khonchaiyaphum. Analysis of finite-time stability in genetic regulatory networks with interval time-varying delays and leakage delay effects[J]. AIMS Mathematics, 2024, 9(9): 25028-25048. doi: 10.3934/math.20241220

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Abstract

We primarily examined the effect of leakage delays on finite-time stability problems for genetic regulatory networks with interval time-varying delays. Since leakage delays can occur within the negative feedback components of networks and significantly impact their dynamics, they may potentially cause instability or suboptimal performance. The derived criteria encompass both leakage delays and discrete interval time-varying delays through the construction of a Lyapunov-Krasovskii function. We employed the estimation of various integral inequalities and a reciprocally convex technique. Additionally, these models consider lower bounds on delays, which may be either positive or zero, and allow for the derivatives of delays to be either positive or negative. Consequently, new criteria for genetic regulatory networks with interval time-varying delays under the effect of leakage delays are expressed in the form of linear matrix inequalities. Ultimately, a numerical example is presented to show the effect of leakage delays and to emphasize the significance of our theoretical findings.

References

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