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Tính ổn định tổng quát cho hệ thống mạng nơ-ron Cohen–Grossberg
Arabian Journal of Mathematics - Trang 1-15 - 2023
Tóm tắt
Bài báo này đề cập đến một hệ thống mạng nơ-ron Cohen–Grossberg (CGNNs) có xem xét các độ trễ phân tán và rời rạc. Lớp các hạt độ trễ đảm bảo tính ổn định mũ có trong các tài liệu trước đó đã được mở rộng đến một lớp hàm mở rộng đảm bảo các loại ổn định tổng quát hơn. Tính ổn định kiểu mũ và kiểu đa thức (hoặc kiểu lũy thừa) trở thành các trường hợp đặc biệt của kết quả của chúng tôi. Điều này được thực hiện bằng cách sử dụng các hàm Lyapunov thích hợp và các đặc điểm của lớp được xem xét.
Từ khóa
#mạng nơ-ron Cohen–Grossberg #độ trễ phân tán #độ trễ rời rạc #tính ổn định mũ #hàm LyapunovTài liệu tham khảo
Bouzerdoum, A.; Pattison, T.R.: Neural network for quadratic optimization with bound constraints. IEEE Trans. Neural Netw. 4(3), 293–304 (1993)
Cohen, M.; Grossberg, S.: Absolute stability and global pattern formation and parallel memory storage by competitive neural networks. IEEE Trans. Syst. Man Cybern. 13(5), 815–826 (1983)
Cui, B.T.; Wu, W.: Global exponential stability of Cohen-Grossberg neural networks with distributed delays. Neurocomputing. 72(1–3), 386–391 (2008)
Faria, T.; Oliveira, J.J.: General criteria for asymptotic and exponential stabilities of neural network models with unbounded delays. Appl. Math. Comput. 217(23), 9646–9658 (2011)
Faria, T.; Gadotti, M.C.; Oliveira, J.J.: Stability results for impulsive functional differential equations with infinite delay. Nonlinear Anal. Theory Methods Appl. 75(18), 6570–6587 (2012)
Grossberg, S.: Nonlinear neural networks: principles, mechanisms, and architectures. Neural Netw. 1(1), 17–61 (1988)
Hopfield, J.J.: Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. 79(8), 2554–2558 (1982)
Hopfield, J.J.; Tank, D.W.: Computing with neural circuits: a model. Science. 233(4764), 625–633 (1986)
Kennedy, M.P.; Chua, L.O.: Neural networks for nonlinear programming. IEEE Trans. Circ. Syst. 35(5), 554–562 (1988)
Kosko, B.: Neural Networks and Fuzzy Systems: A Dynamical System Approach Machine Intelligence. Prentice Hall, Englewood Cliffs (1992)
Lim, J.S.: Reservoir properties determination using fuzzy logic and neural networks from well data in offshore Korea. J. Pet. Sci. Engi. 49(3–4), 182–192 (2005)
Liu, X.; Jiang, N.: Robust stability analysis of generalized neural networks with multiple discrete delays and multiple distributed delays. Neurocomputing. 72(7–9), 1789–1796 (2009)
Park, J.: On global stability criterion of neural networks with continuously distributed delays. Chaos Solit. Fractals. 37(2), 444–449 (2008)
Ping, Z.W.; Lu, J.G.: Global exponential stability of impulsive Cohen-Grossberg neural networks with continuously distributed delays. Chaos Solit. Fractals. 41(1), 164–174 (2009)
Silva, P.C.; Maschio, C.; Schiozer, D.J.: Use of neuro-simulation techniques as proxies to reservoir simulator: application in production history matching. J. Pet. Sci. Eng. 57(3–4), 273–280 (2007)
Song, Q.; Cao, J.: Stability analysis of Cohen–Grossberg neural network with both time-varying and continuously distributed delays. J. Comput. Appl. Math. 197(1), 188–203 (2006)
Verma, A.K., Cheadle, B.A., Routray, A., Mohanty, W.K., Mansinha, L.: Porosity and permeability estimation using neural network approach from well log data. Search Discov. Article #41276 (2014)
Wang, L.: Stability of Cohen–Grossberg neural networks with distributed delays. Appl. Math. Comput. 160(1), 93–110 (2005)
Wu, W.; Cui, B.T.; Lou, X.Y.: Global exponential stability of Cohen–Grossberg neural networks with distributed delays. Math. Comput Model. 47(9–10), 868–873 (2008)
Xu, D.; Wang, X.: A new nonlinear integro-differential inequality and its application. Appl. Math. Lett. 22(11), 1721–1726 (2009)
Xiong, W.J.; Cao, J.D.: Absolutely exponential stability of Cohen–Grossberg neural networks with unbounded delays. Neurocomputing 68(1), 1–12 (2005)
Zhang, Q.; Wei, X.P.; Xu, J.: Global exponential stability of Hopfield neural networks with continuously distributed delays. Phys. Lett. A. 315(6), 431–436 (2003)
Zhao, Y.; Lu, Q.; Feng, Z.: Stability for the mix-delayed Cohen–Grossberg neural networks with nonlinear impulse. J. Syst. Sci. Complex. 23(3), 665–680 (2010)
Zhou, Q.; Shao, J.: Convergence of Cohen–Grossberg neural networks with delays and time-varying coefficients. Electron. J. Differ. Equ. 2008(73), 1–7 (2008)