Global Asymptotic Stability for a New Class of Neutral Neural Networks

Ricai Luo; Gang Lin; Dongdong Yin

doi:doi:10.11648/j.ijamtp.20180403.13

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Global Asymptotic Stability for a New Class of Neutral Neural Networks

Ricai Luo, Gang Lin, Dongdong Yin

Published in International Journal of Applied Mathematics and Theoretical Physics (Volume 4, Issue 3)

Received: 28 August 2018 Accepted: 17 October 2018 Published: 9 November 2018

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Abstract

In the present world, due to the complicated dynamic properties of neural cells, many dynamic neural networks are described by neutral functional differential equations including neutral delay differential equations. These neural networks are called neutral neural networks or neural networks of neural-type. The differential expression not only defines the derivative term of the current state but also explains the derivative term of the past state. In this paper, global asymptotic stability of a neutral-type neural networks, with time-varying delays, are presented and analyzed. The neural network is made up of parts that include: linear, non-linear, non-linear delayed, time delays in time derivative states, as well as a part of activation function with the derivative. Different from prior references, as part of the considered networks, the last part involves an activation function with the derivative rather than multiple delays; that is a new class of neutral neural networks. This paper assumes that the activation functions satisfy the Lipschitz conditions so that the considered system has a unique equilibrium point. By constructing a Lyapunov-Krasovskii-type function and by using a linear matrix inequality analysis technique, a sufficient condition for global asymptotic stability of this neural network has been obtained. Finally, we present a numerical example to show the effectiveness and applicability of the proposed approach.

Published in	International Journal of Applied Mathematics and Theoretical Physics (Volume 4, Issue 3)
DOI	10.11648/j.ijamtp.20180403.13
Page(s)	78-83
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2018. Published by Science Publishing Group

Keywords

Global Asymptotic Stability, Neutral Neural Network, Time-Varying Delay, Sufficient Condition

References

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APA Style

Ricai Luo, Gang Lin, Dongdong Yin. (2018). Global Asymptotic Stability for a New Class of Neutral Neural Networks. International Journal of Applied Mathematics and Theoretical Physics, 4(3), 78-83. https://doi.org/10.11648/j.ijamtp.20180403.13

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ACS Style

Ricai Luo; Gang Lin; Dongdong Yin. Global Asymptotic Stability for a New Class of Neutral Neural Networks. Int. J. Appl. Math. Theor. Phys. 2018, 4(3), 78-83. doi: 10.11648/j.ijamtp.20180403.13

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AMA Style

Ricai Luo, Gang Lin, Dongdong Yin. Global Asymptotic Stability for a New Class of Neutral Neural Networks. Int J Appl Math Theor Phys. 2018;4(3):78-83. doi: 10.11648/j.ijamtp.20180403.13

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@article{10.11648/j.ijamtp.20180403.13,
  author = {Ricai Luo and Gang Lin and Dongdong Yin},
  title = {Global Asymptotic Stability for a New Class of Neutral Neural Networks},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {4},
  number = {3},
  pages = {78-83},
  doi = {10.11648/j.ijamtp.20180403.13},
  url = {https://doi.org/10.11648/j.ijamtp.20180403.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20180403.13},
  abstract = {In the present world, due to the complicated dynamic properties of neural cells, many dynamic neural networks are described by neutral functional differential equations including neutral delay differential equations. These neural networks are called neutral neural networks or neural networks of neural-type. The differential expression not only defines the derivative term of the current state but also explains the derivative term of the past state. In this paper, global asymptotic stability of a neutral-type neural networks, with time-varying delays, are presented and analyzed. The neural network is made up of parts that include: linear, non-linear, non-linear delayed, time delays in time derivative states, as well as a part of activation function with the derivative. Different from prior references, as part of the considered networks, the last part involves an activation function with the derivative rather than multiple delays; that is a new class of neutral neural networks. This paper assumes that the activation functions satisfy the Lipschitz conditions so that the considered system has a unique equilibrium point. By constructing a Lyapunov-Krasovskii-type function and by using a linear matrix inequality analysis technique, a sufficient condition for global asymptotic stability of this neural network has been obtained. Finally, we present a numerical example to show the effectiveness and applicability of the proposed approach.},
 year = {2018}
}

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TY  - JOUR
T1  - Global Asymptotic Stability for a New Class of Neutral Neural Networks
AU  - Ricai Luo
AU  - Gang Lin
AU  - Dongdong Yin
Y1  - 2018/11/09
PY  - 2018
N1  - https://doi.org/10.11648/j.ijamtp.20180403.13
DO  - 10.11648/j.ijamtp.20180403.13
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 78
EP  - 83
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20180403.13
AB  - In the present world, due to the complicated dynamic properties of neural cells, many dynamic neural networks are described by neutral functional differential equations including neutral delay differential equations. These neural networks are called neutral neural networks or neural networks of neural-type. The differential expression not only defines the derivative term of the current state but also explains the derivative term of the past state. In this paper, global asymptotic stability of a neutral-type neural networks, with time-varying delays, are presented and analyzed. The neural network is made up of parts that include: linear, non-linear, non-linear delayed, time delays in time derivative states, as well as a part of activation function with the derivative. Different from prior references, as part of the considered networks, the last part involves an activation function with the derivative rather than multiple delays; that is a new class of neutral neural networks. This paper assumes that the activation functions satisfy the Lipschitz conditions so that the considered system has a unique equilibrium point. By constructing a Lyapunov-Krasovskii-type function and by using a linear matrix inequality analysis technique, a sufficient condition for global asymptotic stability of this neural network has been obtained. Finally, we present a numerical example to show the effectiveness and applicability of the proposed approach.
VL  - 4
IS  - 3
ER  -

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Author Information

Ricai Luo

School of Mathematics and Statistics, Hechi University, Yizhou, China
Gang Lin

School of Design and Built Environment, Curtin University, Perth, Australia
Dongdong Yin

School of Mathematics and Statistics, Hechi University, Yizhou, China

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Plain Text BibTeX RIS

APA Style

Ricai Luo, Gang Lin, Dongdong Yin. (2018). Global Asymptotic Stability for a New Class of Neutral Neural Networks. International Journal of Applied Mathematics and Theoretical Physics, 4(3), 78-83. https://doi.org/10.11648/j.ijamtp.20180403.13

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ACS Style

Ricai Luo; Gang Lin; Dongdong Yin. Global Asymptotic Stability for a New Class of Neutral Neural Networks. Int. J. Appl. Math. Theor. Phys. 2018, 4(3), 78-83. doi: 10.11648/j.ijamtp.20180403.13

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AMA Style

Ricai Luo, Gang Lin, Dongdong Yin. Global Asymptotic Stability for a New Class of Neutral Neural Networks. Int J Appl Math Theor Phys. 2018;4(3):78-83. doi: 10.11648/j.ijamtp.20180403.13

Copy | Download

@article{10.11648/j.ijamtp.20180403.13,
  author = {Ricai Luo and Gang Lin and Dongdong Yin},
  title = {Global Asymptotic Stability for a New Class of Neutral Neural Networks},
  journal = {International Journal of Applied Mathematics and Theoretical Physics},
  volume = {4},
  number = {3},
  pages = {78-83},
  doi = {10.11648/j.ijamtp.20180403.13},
  url = {https://doi.org/10.11648/j.ijamtp.20180403.13},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijamtp.20180403.13},
  abstract = {In the present world, due to the complicated dynamic properties of neural cells, many dynamic neural networks are described by neutral functional differential equations including neutral delay differential equations. These neural networks are called neutral neural networks or neural networks of neural-type. The differential expression not only defines the derivative term of the current state but also explains the derivative term of the past state. In this paper, global asymptotic stability of a neutral-type neural networks, with time-varying delays, are presented and analyzed. The neural network is made up of parts that include: linear, non-linear, non-linear delayed, time delays in time derivative states, as well as a part of activation function with the derivative. Different from prior references, as part of the considered networks, the last part involves an activation function with the derivative rather than multiple delays; that is a new class of neutral neural networks. This paper assumes that the activation functions satisfy the Lipschitz conditions so that the considered system has a unique equilibrium point. By constructing a Lyapunov-Krasovskii-type function and by using a linear matrix inequality analysis technique, a sufficient condition for global asymptotic stability of this neural network has been obtained. Finally, we present a numerical example to show the effectiveness and applicability of the proposed approach.},
 year = {2018}
}

Copy | Download

TY  - JOUR
T1  - Global Asymptotic Stability for a New Class of Neutral Neural Networks
AU  - Ricai Luo
AU  - Gang Lin
AU  - Dongdong Yin
Y1  - 2018/11/09
PY  - 2018
N1  - https://doi.org/10.11648/j.ijamtp.20180403.13
DO  - 10.11648/j.ijamtp.20180403.13
T2  - International Journal of Applied Mathematics and Theoretical Physics
JF  - International Journal of Applied Mathematics and Theoretical Physics
JO  - International Journal of Applied Mathematics and Theoretical Physics
SP  - 78
EP  - 83
PB  - Science Publishing Group
SN  - 2575-5927
UR  - https://doi.org/10.11648/j.ijamtp.20180403.13
AB  - In the present world, due to the complicated dynamic properties of neural cells, many dynamic neural networks are described by neutral functional differential equations including neutral delay differential equations. These neural networks are called neutral neural networks or neural networks of neural-type. The differential expression not only defines the derivative term of the current state but also explains the derivative term of the past state. In this paper, global asymptotic stability of a neutral-type neural networks, with time-varying delays, are presented and analyzed. The neural network is made up of parts that include: linear, non-linear, non-linear delayed, time delays in time derivative states, as well as a part of activation function with the derivative. Different from prior references, as part of the considered networks, the last part involves an activation function with the derivative rather than multiple delays; that is a new class of neutral neural networks. This paper assumes that the activation functions satisfy the Lipschitz conditions so that the considered system has a unique equilibrium point. By constructing a Lyapunov-Krasovskii-type function and by using a linear matrix inequality analysis technique, a sufficient condition for global asymptotic stability of this neural network has been obtained. Finally, we present a numerical example to show the effectiveness and applicability of the proposed approach.
VL  - 4
IS  - 3
ER  -

Copy | Download