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題名 具時間延遲之耦合反應擴散神經網路的有界性與絕對穩定性
Boundedness and absolute stability of coupled reaction-diffusion neural networks with time delays
作者 何明霖
Ho, Min-Lin
貢獻者 曾睿彬
Tseng, Jui-Pin
何明霖
Ho, Min-Lin
關鍵詞 神經網路
反應擴散
絕對穩定性
有界性
主從
Neural network
Reaction-diffusion
Absolute stability
Boundedness
Master-slave
日期 2023
上傳時間 1-Feb-2023 13:48:52 (UTC+8)
摘要 在本論文中，我們考慮了一類由兩個反應擴散神經網路所組成的具有時
間延遲耦合系統。兩個神經網路是以主從的方式耦合。我們首先討論耦合
反應擴散神經網路之解的有界性。然後，我們進一步建立耦合反應擴散神
經網路的絕對穩定性。有界性與絕對穩定性的判別法可以用簡單的計算檢
驗。
In the thesis, we consider a class of coupled systems consisting of two reaction-diffusion neural networks with transmission time delays. These two neral networks
are coupled in a master-slave manner. First, we discuss the boundedness of the solutions of the coupled reaction-diffusion neural networks. Then, we further establish the absolute stability of the coupled reaction-diffusion neural networks. The boundedness and absolute stability criteria can be verified with simple computa-
tions.
參考文獻 Reference

[1] ABIODUN, O. I., JANTAN, A., OMOLARA, A. E., DADA, K. V., MOHAMED, N. A.,
AND ARSHAD, H. State-of-the-art in artificial neural network applications: A survey. Heliyon 4, 11 (2018), e00938.

[2] COHEN, M. A., AND GROSSBERG, S. Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE transactions on systems, man, and cybernetics, 5 (1983), 815–826.

[3] FAUGERAS, O., GRIMBERT, F., AND SLOTINE, J.-J. Absolute stability and complete synchronization in a class of neural fields models. SIAM Journal on applied mathematics 69, 1 (2008), 205–250.

[4] HAEUSLER, S., AND MAASS, W. A statistical analysis of information-processing properties of lamina-specific cortical microcircuit models. Cerebral cortex 17, 1 (2007), 149–162.

[5] HAN, Q.-L. Absolute stability of time-delay systems with sector-bounded nonlinearity. Automatica 41, 12 (2005), 2171–2176.

[6] HU, C., YU, J., JIANG, H., AND TENG, Z. Exponential synchronization for reaction–diffusion networks with mixed delays in terms of p-norm via intermittent driving. Neural Networks 31 (2012), 1–11.

[7] JANSEN, B. H., ZOURIDAKIS, G., AND BRANDT, M. E. A neurophysiologically-based mathematical model of flash visual evoked potentials. Biological cybernetics 68, 3 (1993), 275–283.

[8] KAO, C.-Y., SHIH, C.-W., AND WU, C.-H. Absolute stability and synchronization
in neural field models with transmission delays. Physica D: Nonlinear Phenomena 328(2016), 21–33.

[9] LIU, X. Synchronization of linearly coupled neural networks with reaction–diffusion terms and unbounded time delays. Neurocomputing 73, 13-15 (2010),2681–2688.

[10] MILLER, A., BLOTT, B., ET AL. Review of neural network applications in medical
imaging and signal processing. Medical and Biological Engineering and Computing 30,5 (1992), 449–464.

[11] NOGUCHI, N., WILL, J., REID, J., AND ZHANG, Q. Development of a master–slave robot system for farm operations. Computers and Electronics in agriculture 44, 1 (2004),1–19.

[12] POPOV, V. On absolute stability of non-linear automatic control systems. Automatika i Telemekhanika 22, 8 (1961), 961–979.

[13] RICHARD, J.-P. Time-delay systems: an overview of some recent advances and open problems. automatica 39, 10 (2003), 1667–1694.

[14] SHAHIN, M. A., JAKSA, M. B., AND MAIER, H. R. Artificial neural network applications in geotechnical engineering. Australian geomechanics 36, 1 (2001), 49–62.

[15] THOMSON, A. M., AND BANNISTER, A. P. Interlaminar connections in the neocortex.Cerebral cortex 13, 1 (2003), 5–14.

[16] TSENG, J.-P. Global synchronization of coupled reaction–diffusion neural networks with general couplings via an iterative approach. IMA Journal of Applied Mathematics 85, 4 (2020), 635–669.

[17] VAN ROTTERDAM, A., DA SILVA, F. L., VAN DEN ENDE, J., VIERGEVER, M., AND HERMANS, A. A model of the spatial-temporal characteristics of the alpha rhythm. Bulletin of mathematical biology 44, 2 (1982), 283–305.

[18] WANG, J.-L., WU, H.-N., AND GUO, L. Novel adaptive strategies for synchronization of linearly coupled neural networks with reaction-diffusion terms. IEEE Transactions on Neural Networks and Learning Systems 25, 2 (2013), 429–440.

[19] WIDROW, B., RUMELHART, D. E., AND LEHR, M. A. Neural networks: applications in industry, business and science. Communications of the ACM 37, 3 (1994), 93–106.

[20] WONG, B. K., BODNOVICH, T. A., AND SELVI, Y. Neural network applications in
business: A review and analysis of the literature (1988–1995). Decision Support Systems19, 4 (1997), 301–320.

[21] YANG, X., CAO, J., AND YANG, Z. Synchronization of coupled reaction-diffusion neural networks with time-varying delays via pinning-impulsive controller. SIAM Journal on Control and Optimization 51, 5 (2013), 3486–3510.

[22] ZHANG, H., ZENG, Z., AND HAN, Q.-L. Synchronization of multiple reaction–diffusion neural networks with heterogeneous and unbounded time-varying delays. IEEE Transactions on Cybernetics 49, 8 (2018), 2980–2991.

[23] ZHANG, Y.-C. Boundedness and synchronization of master-slave reaction-diffusion neural networks with time delays. Unpublished master’s thesis. National Chengchi University(2022).
描述 碩士
國立政治大學
應用數學系
108751009
資料來源 http://thesis.lib.nccu.edu.tw/record/#G0108751009
資料類型 thesis
dc.contributor.advisor 曾睿彬zh_TW
dc.contributor.advisor Tseng, Jui-Pinen_US
dc.contributor.author (Authors) 何明霖zh_TW
dc.contributor.author (Authors) Ho, Min-Linen_US
dc.creator (作者) 何明霖zh_TW
dc.creator (作者) Ho, Min-Linen_US
dc.date (日期) 2023en_US
dc.date.accessioned 1-Feb-2023 13:48:52 (UTC+8)-
dc.date.available 1-Feb-2023 13:48:52 (UTC+8)-
dc.date.issued (上傳時間) 1-Feb-2023 13:48:52 (UTC+8)-
dc.identifier (Other Identifiers) G0108751009en_US
dc.identifier.uri (URI) http://nccur.lib.nccu.edu.tw/handle/140.119/143171-
dc.description (描述) 碩士zh_TW
dc.description (描述) 國立政治大學zh_TW
dc.description (描述) 應用數學系zh_TW
dc.description (描述) 108751009zh_TW
dc.description.abstract (摘要) 在本論文中，我們考慮了一類由兩個反應擴散神經網路所組成的具有時
間延遲耦合系統。兩個神經網路是以主從的方式耦合。我們首先討論耦合
反應擴散神經網路之解的有界性。然後，我們進一步建立耦合反應擴散神
經網路的絕對穩定性。有界性與絕對穩定性的判別法可以用簡單的計算檢
驗。		zh_TW
dc.description.abstract (摘要) In the thesis, we consider a class of coupled systems consisting of two reaction-diffusion neural networks with transmission time delays. These two neral networks
are coupled in a master-slave manner. First, we discuss the boundedness of the solutions of the coupled reaction-diffusion neural networks. Then, we further establish the absolute stability of the coupled reaction-diffusion neural networks. The boundedness and absolute stability criteria can be verified with simple computa-
tions.		en_US
dc.description.tableofcontents Contents
誌謝 i
中文摘要 ii
Abstract iii
Contents iv
1 Introduction 1
2 Preliminaries 5
3 Main results 8
3.1 Boundedness of solutions 8
3.2 Absolute stability 20
4 Examples 32
5 Conclusions 35
Reference 36		zh_TW
dc.format.extent 808281 bytes-
dc.format.mimetype application/pdf-
dc.source.uri (資料來源) http://thesis.lib.nccu.edu.tw/record/#G0108751009en_US
dc.subject (關鍵詞) 神經網路zh_TW
dc.subject (關鍵詞) 反應擴散zh_TW
dc.subject (關鍵詞) 絕對穩定性zh_TW
dc.subject (關鍵詞) 有界性zh_TW
dc.subject (關鍵詞) 主從zh_TW
dc.subject (關鍵詞) Neural networken_US
dc.subject (關鍵詞) Reaction-diffusionen_US
dc.subject (關鍵詞) Absolute stabilityen_US
dc.subject (關鍵詞) Boundednessen_US
dc.subject (關鍵詞) Master-slaveen_US
dc.title (題名) 具時間延遲之耦合反應擴散神經網路的有界性與絕對穩定性zh_TW
dc.title (題名) Boundedness and absolute stability of coupled reaction-diffusion neural networks with time delaysen_US
dc.type (資料類型) thesisen_US
dc.relation.reference (參考文獻) Reference

[1] ABIODUN, O. I., JANTAN, A., OMOLARA, A. E., DADA, K. V., MOHAMED, N. A.,
AND ARSHAD, H. State-of-the-art in artificial neural network applications: A survey. Heliyon 4, 11 (2018), e00938.

[2] COHEN, M. A., AND GROSSBERG, S. Absolute stability of global pattern formation and parallel memory storage by competitive neural networks. IEEE transactions on systems, man, and cybernetics, 5 (1983), 815–826.

[3] FAUGERAS, O., GRIMBERT, F., AND SLOTINE, J.-J. Absolute stability and complete synchronization in a class of neural fields models. SIAM Journal on applied mathematics 69, 1 (2008), 205–250.

[4] HAEUSLER, S., AND MAASS, W. A statistical analysis of information-processing properties of lamina-specific cortical microcircuit models. Cerebral cortex 17, 1 (2007), 149–162.

[5] HAN, Q.-L. Absolute stability of time-delay systems with sector-bounded nonlinearity. Automatica 41, 12 (2005), 2171–2176.

[6] HU, C., YU, J., JIANG, H., AND TENG, Z. Exponential synchronization for reaction–diffusion networks with mixed delays in terms of p-norm via intermittent driving. Neural Networks 31 (2012), 1–11.

[7] JANSEN, B. H., ZOURIDAKIS, G., AND BRANDT, M. E. A neurophysiologically-based mathematical model of flash visual evoked potentials. Biological cybernetics 68, 3 (1993), 275–283.

[8] KAO, C.-Y., SHIH, C.-W., AND WU, C.-H. Absolute stability and synchronization
in neural field models with transmission delays. Physica D: Nonlinear Phenomena 328(2016), 21–33.

[9] LIU, X. Synchronization of linearly coupled neural networks with reaction–diffusion terms and unbounded time delays. Neurocomputing 73, 13-15 (2010),2681–2688.

[10] MILLER, A., BLOTT, B., ET AL. Review of neural network applications in medical
imaging and signal processing. Medical and Biological Engineering and Computing 30,5 (1992), 449–464.

[11] NOGUCHI, N., WILL, J., REID, J., AND ZHANG, Q. Development of a master–slave robot system for farm operations. Computers and Electronics in agriculture 44, 1 (2004),1–19.

[12] POPOV, V. On absolute stability of non-linear automatic control systems. Automatika i Telemekhanika 22, 8 (1961), 961–979.

[13] RICHARD, J.-P. Time-delay systems: an overview of some recent advances and open problems. automatica 39, 10 (2003), 1667–1694.

[14] SHAHIN, M. A., JAKSA, M. B., AND MAIER, H. R. Artificial neural network applications in geotechnical engineering. Australian geomechanics 36, 1 (2001), 49–62.

[15] THOMSON, A. M., AND BANNISTER, A. P. Interlaminar connections in the neocortex.Cerebral cortex 13, 1 (2003), 5–14.

[16] TSENG, J.-P. Global synchronization of coupled reaction–diffusion neural networks with general couplings via an iterative approach. IMA Journal of Applied Mathematics 85, 4 (2020), 635–669.

[17] VAN ROTTERDAM, A., DA SILVA, F. L., VAN DEN ENDE, J., VIERGEVER, M., AND HERMANS, A. A model of the spatial-temporal characteristics of the alpha rhythm. Bulletin of mathematical biology 44, 2 (1982), 283–305.

[18] WANG, J.-L., WU, H.-N., AND GUO, L. Novel adaptive strategies for synchronization of linearly coupled neural networks with reaction-diffusion terms. IEEE Transactions on Neural Networks and Learning Systems 25, 2 (2013), 429–440.

[19] WIDROW, B., RUMELHART, D. E., AND LEHR, M. A. Neural networks: applications in industry, business and science. Communications of the ACM 37, 3 (1994), 93–106.

[20] WONG, B. K., BODNOVICH, T. A., AND SELVI, Y. Neural network applications in
business: A review and analysis of the literature (1988–1995). Decision Support Systems19, 4 (1997), 301–320.

[21] YANG, X., CAO, J., AND YANG, Z. Synchronization of coupled reaction-diffusion neural networks with time-varying delays via pinning-impulsive controller. SIAM Journal on Control and Optimization 51, 5 (2013), 3486–3510.

[22] ZHANG, H., ZENG, Z., AND HAN, Q.-L. Synchronization of multiple reaction–diffusion neural networks with heterogeneous and unbounded time-varying delays. IEEE Transactions on Cybernetics 49, 8 (2018), 2980–2991.

[23] ZHANG, Y.-C. Boundedness and synchronization of master-slave reaction-diffusion neural networks with time delays. Unpublished master’s thesis. National Chengchi University(2022).		zh_TW