具時間延遲之主從反應擴散神經網絡的有界性與同步化

Boundedness and synchronization of master-slave reaction-diffusion neural networks with time delays

張又權(Zhang Yo-Cheng)

指導教授 ： 曾睿彬

國立政治大學/理學院/應用數學系/碩士(2022年)

https://doi.org/10.6814/NCCU202200851

摘要

在本文中，我們考慮了具有時間延遲的主從反應-擴散神經網絡。我們
考慮的網絡可以是離散型時間延遲和分布型時間延遲。我們首先建立所考慮系統的解的有界性。然後，我們進一步研究了所考慮系統的全局同步化。

關鍵字

神經網絡 ； 主從系統 ； 時間延遲 ； 有界性 ； 全局同步化

並列摘要

In this paper, we consider master-slave reaction-diffusion neural networks with time delays. The networks we consider can be with both discrete delays and distributed delays. We first establish the boundedness of the solutions of the considered systems. Then, we further investigate the global synchronization of the considered sysems.

並列關鍵字

Neural network ； Master-slave system ； Time delays ； Boundedness ； Global synchronization

參考文獻

[1] J. Arrieta. On boundedness of solutions of reaction-diffusion equations with nonlinear boundary conditions. Proceedings of the American Mathematical Society, 136(1):151–160, 2008.

[2] S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.U. Hwang. Complex networks: Structure and dynamics. Physics reports, 424(4-5):175–308, 2006.

[3] S. Dharani, R. Rakkiyappan, J.D. Cao, and A. Alsaedi. Synchronization of generalized reaction-diffusion neural networks with time-varying delays based on general integral inequalities and sampled-data control approach. Cognitive neurodynamics, 11(4):369–381, 2017.

[4] Q.T. Gan, T.L. Liu, C. Liu, and T.S. Lv. Synchronization for a class of generalized neural networks with interval time-varying delays and reaction-diffusion terms. Nonlinear

analysis: modelling and control, 21(3):379–399, 2016.