Controlling stability through the rate of decay of the delay feedback kernels

Mohammed D. Kassim; Mohammed D. Kassim

doi:10.3934/math.20231344

AIMS Mathematics

2023, Volume 8, Issue 11: 26343-26356. doi: 10.3934/math.20231344

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Research article

Controlling stability through the rate of decay of the delay feedback kernels

Mohammed D. Kassim ^,

Department of Basic Engineering Sciences, College of Engineering, Imam Abdulrahman Bin Faisal University, P. O. Box 1982, Dammam 34151, Saudi Arabia

Received: 02 August 2023 Revised: 30 August 2023 Accepted: 07 September 2023 Published: 14 September 2023
MSC : 34C11, 34G20, 92B20

Of concern is the Hopfield neural network system comprising discrete as well as distributed delays in the form of a convolution. For a desired convergence rate of the solution to the equilibrium state, we establish sufficient conditions on the delay kernels ensuring this matter. Our result improves an existing one in the literature. The adopted approach is completely different. It relies on a judicious choice of a Lyapunov-like function and careful manipulations.
- Hopfield neural network system,
- discrete delay,
- distributed delay,
- exponentail stability,
- arbitrary stability,
- Lyapunov-type function
Citation: Mohammed D. Kassim. Controlling stability through the rate of decay of the delay feedback kernels[J]. AIMS Mathematics, 2023, 8(11): 26343-26356. doi: 10.3934/math.20231344

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Abstract

Of concern is the Hopfield neural network system comprising discrete as well as distributed delays in the form of a convolution. For a desired convergence rate of the solution to the equilibrium state, we establish sufficient conditions on the delay kernels ensuring this matter. Our result improves an existing one in the literature. The adopted approach is completely different. It relies on a judicious choice of a Lyapunov-like function and careful manipulations.

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