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| تعداد نشریات | 37 |
| تعداد شماره‌ها | 1,001 |
| تعداد مقالات | 8,542 |
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| تعداد دریافت فایل اصل مقاله | 10,720,258 |
Global Asymptotic and Exponential Stability of Tri-Cell Networks with Different Time Delays | ||
| Control and Optimization in Applied Mathematics | ||
| مقاله 4، دوره 2، شماره 2، اسفند 2017، صفحه 45-60 اصل مقاله (642.75 K) | ||
| نوع مقاله: Research Article | ||
| نویسندگان | ||
| Zohreh Dadi* ؛ Farzaneh Ravanbakhsh | ||
| Department of Mathematics, Faculty of Basic Sciences, University of Bojnord, P.O. Box 1339, Bojnord 94531, Iran | ||
| چکیده | ||
| In this paper, a bidirectional ring network with three cells and different time delays is presented. To propose this model which is a good extension of three-unit neural networks, coupled cell network theory and neural network theory are applied. In this model, every cell has self-connections without delay but different time delays are assumed in other connections. A suitable Lyapunov function is presented for this model which helps to get sufficient conditions to guarantee asymptotic and exponential stability of the model. Also, these conditions are independent of time delays. Finally, analytical results are confirmed by numerical examples which are stated. | ||
| کلیدواژه‌ها | ||
| Asymptotic stability؛ Exponential stability؛ Nonlinear systems؛ Cell network | ||
| عنوان مقاله [English] | ||
| پایداری مجانبی و نمایی سراسری شبکه های سه سلولی با تاخیرهای زمانی متفارت | ||
| نویسندگان [English] | ||
| زهره دادی؛ فرزانه روان بخش | ||
| دانشگاه بجنورد | ||
| چکیده [English] | ||
| در این مقاله، یک شبکه حلقوی دوطرفه با ۳ سلول و تاخیرهای زمانی متفاوت ارایه شده است. برای ارایه این مدل که تعمیمی مناسب از شبکه های عصبی ۳ نرونی است، نظریه شبکه سلولی درگیر و شبکه عصبی اعمال می‌شود. در این مدل، هرسلول دارای خود اتصالی های بدون تاخیر است و بقیه اتصالات با تاخیر فرض شده است. یک تابع لیاپونف مناسب برای مدل ارائه شده که در کسب شرایط کافی برای تضمین پایداری نمایی و مجانبی مدل به ما کمک می کند. همچنین این شرایط مستقل از تاخیرهای زمانی است. سرانجام نتایج تحلیلی با مثالهای عددی که بیان می‌شوند تایید شده اند. | ||
| کلیدواژه‌ها [English] | ||
| پایداری مجانبی, پایداری نمایی, دستگاههای غیرخطی, شبکه سلولی | ||
| مراجع | ||
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bibitem{R1}
Ahmadkhanlou F., Adeli H. (2005). ``Optimum cost design of reinforced concrete slabs using neural dynamics model", Engineering Applications of Artificial Intelligence, 18, 65--72. bibitem{R2} Amari S.I., Cichocki A. (1998). ``Adaptive blind signal processing-neural network approaches", Proceedings of the IEEE, 86, 2026--2048. bibitem{ZD} Dadi Z. (2017). ``Dynamics of two-cell systems with discrete delays", Advances in Computational Mathematics, 43:3, 653--676. bibitem{G2} Golubitsky M., Pivato M., Stewart I. (2004). ``Interior symmetry and local bifurcation in coupled cell networks", Dynamical Systems, 19:4, 389--407. bibitem{G3} Golubitsky M., Stewart I. (2006). ``Nonlinear dynamics of networks: the groupoid formalism", Bulletin of the American Mathematical Society, 43, 305--364. bibitem{G} Golubitsky M., Stewart I., Buono P.L., Collins J.J. (1998). ``A modular network for legged locomotion", Physica D, 115, 56--72. bibitem{G4} Golubitsky M., Stewart I., T"{o}r"{o}k A. (2005). ``Patterns of synchrony in coupled cell networks with multiple arrows", SIAM Journal on Applied Dynamical Systems, 4:1, 78--100. bibitem{R3} Guo S., Huang L. (2003). ``Hopf bifurcating periodic orbits in a ring of neurons with delays", Physica D, 183, 19--44. bibitem{dj} Javidmanesh E., Dadi Z., Afsharnezhad Z., Effati S. (2014). ``Global stability analysis and existence of periodic solutions in an eight-neuron BAM neural network model with delays", Journal of Intelligent and Fuzzy Systems, 27:1, 391--406. bibitem{R4} Jiang F., Shen J., Li X. (2013) ``The LMI method for stationary oscillation of interval neural networks with three neuron activations under impulsive effects", Nonlinear Analysis: Real World Applications, 14:3, 1404--1416. bibitem{R5} Kwon O.M., Kwon J.W., Kim S.H. (2011). ``New results on stability criteria for neural networks with time-varying delays", Chinese Physics B, 20:5, 050505. bibitem{R6} Kwon O.M., Park M., Lee S.M., Park J.H., Cha E.J. (2013). ``Stability for neural networks with time-varying delay via some new approaches", IEEE Transactions on Neural Networks and Learning Systems, 24:2, 181--193. bibitem{R7} Li H., Liao X., Li C., Huang H., Li C. (2011). ``Edge detection of noisy images based on cellular neural networks", Communications in Nonlinear Science and Numerical Simulations, 16:9, 3746--3759. bibitem{R9} Luo R., Xu H., Wang W.S., Sun J., Xu W. (2016). ``A weak condition for global stability of delayed neural networks", Journal of Industrial and Management Optimization, 12:2, 505--514. bibitem{R10} Shen Y., Wang J. (2012). ``Robustness analysis of global exponential stability of recurrent networks in the presence of time delays and random disturbances", IEEE Transactions on Neural Networks and Learning Systems, 23:1, 87--96. bibitem{R11} Shu Y., Liu X., Liu Y. (2016). ``Stability and passivity analysis for uncertain discrete-time neural networks with time-varying delay", Neurocomputing, 173:3, 1706--1714. bibitem{R12} Song Y., Han M., Wei J. (2005). ``Stability and Hopf bifurcation on a simplified BAM neural network with delays", Physica D: Nonlinear Phenomena, 200, 185--204. bibitem{R13} Tian J., Xie X. (2010). ``New asymptotic stability criteria for neural networks with time varying delay", Physics Letters A, 374:7, 938--943. bibitem{S} Stewart I., Golubitsky M., Pivato M. (2003). ``Symmetry groupoids and patterns of synchrony in coupled cell networks", SIAM Journal on Applied Dynamical Systems, 2:4, 606--646. bibitem{R15} Wei J., Li M.Y. (2004). ``Global existence of periodic solutions in a tri-neuron network model with delays", Physica D, 198, 106--119. bibitem{R16} Wei J.J., Velarde M.G. (2004). ``Bifurcation analysis and existence of periodic solutions in a simple neural network with delays", Chaos, 143, 940--953. bibitem{R17}Yan X.P. (2006). ``Hopf bifurcation and stability for a delayed tri-neuron network model", Journal of Computational and Applied Mathematics, 196, 579--595. bibitem{R8} Yiping L., Lemmert R., Volkmann P. (2001). ``Bifurcation of periodic solution in a three-unit neural network with delay", Acta Mathematicae Applicatae Sinica, 17:3, 375--381. bibitem{R18}Yuan Y. (2007). ``Dynamics in a delayed-neural network", Chaos, Solitons and Fractals, 33:2, 443--454. bibitem{R19} Zeng Z., Huang D.S., Wang Z. (2008). ``Pattern memory analysis based on stability theory of cellular neural networks", Applied Mathematical Modelling, 32:1, 112--121. bibitem{R20} Zeng Z., Wang J. (2007). ``Analysis and design of associative memories based on recurrent neural networks with linear saturation activation functions and time-varying delays", Neural computation, 19:8, 2149--2182. bibitem{R21} Zheng M., Mao Z., Li K., Fei M. (2016). ``Quadratic separation framework for stability analysis of a class of systems with time delays", Neurocomputing, 174, 466--474. bibitem{R22} Zheng C.D., Shan QH, Wang Z. (2012). ``Novel stability criterion for cellular neural networks: an improved Gu's discretized LKF approach", Journal of the Franklin Institute, 349:1, 25--41. bibitem{R23} Zou S., Huang L., Wang Y. (2010). ``Bifurcation of a three-unit neural network", Applied Mathematics and Computation, 217:2, 904--917. | ||
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آمار تعداد مشاهده مقاله: 358 تعداد دریافت فایل اصل مقاله: 200 |
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