Hướng phát triển của luận án

Một phần của tài liệu Phát triển mạng nơron tế bào đa tương tác và khả năng ứng dụng (Trang 111 - 140)

Các nội dung nghiên cứu của luận án có thể tiếp tục hoàn thiện và phát triển, một số hướng phát triển như sau:

i) Mở rộng nghiên cứu thử nghiệm nhận dạng với mô hình mạng tự điều chỉnh cấu hình mạng, tự điều chỉnh các tham số đầu vào, số lượng tham số thích nghị

ii) Nghiên cứu thử nghiệm với các mô hình lai ghép với mạng nơron tích chập và thẻ sinh trắc học.

iii) Tiếp cận hướng nghiên cứu nhằm đảm bảo độ chính xác trong nhận dạng khi ngữ liệu của môi trường thực không hoàn toàn như dữ liệu đã được học.

iv) Kết hợp việc nhận dạng hình ảnh, hành vi, tiếng nói và các giác quan để góp phần hướng tới xây dựng các hệ thống thông minh hoạt động hiệu quả.

v) Tiến tới xây dựng thuật toán học đầy đủ các tham số [A, B, I] cho mạng nơron tế bào bậc caọ

DANH MỤC CÁC CÔNG BỐ CỦA LUẬN ÁN

Ạ1. Nguyen Tai Tuyen, Nguyen Quang Hoan, Ngo Van Sy, (2016) “Stability of Multi-Interactive Cellular Neural Networks Using Lyapunov Function”, Hội thảo toàn quốc về Điện tử, Truyền thông và Công nghệ Thông tin REV-2016, pp.59- 61.

Ạ2. Nguyen Tai Tuyen, (2016) "On A Structure Of High Order Multi-Interaction Cellular Neural Network", International Journal of Advance Computational Engineering and Networking (IJACEN), pp. 24-26, Volume-4, Issue-2.

Ạ3. Tuyen Nguyen Tai, (2017) "On an Application of Multi-Interaction Cellular Neural Network in Smart Farms Systems", International Journal of Electrical, Electronics and Data Communication (IJEEDC), pp. 1-3, Volume-5, Issue-7. Ạ4. Nguyen Tai Tuyen, Nguyen Quang Hoan, (2018) “An Application of Multi-

Interaction Cellular Neural Network on the Basis of STM32 and FPGA”,

International Journal for Research in Applied Science & Engineering Technology (IJRASET), pp. 177-181, Volume-5, Issue-Ị

Ạ5. Tuyen Nguyen Tai, Hoan Nguyen Quang, (2018) “An Application of High Order Multi-Interaction Cellular Neural Network in Early Warning for Cardiovascular Disease Patients with Anti-Vitamin K”, International Journal of Research in Technology and Management, pp. 24-27, Volume-4, Issue-1.

Ạ6. Nguyen Tai Tuyen, Nguyen Quang Hoan, Ngo Van Sy, (2019) “On An Application of High Order MultiInteraction Cellular Neural Network in the Early Fire Warning System”, International Journal of Latest Engineering Science, pp. 53-58, Volume-2, Issue-6.

Ạ7. Nguyen Quang Hoan, Nguyen Tai Tuyen, Duong Duc Anh, (2020) “Architecture and Stability of the Second-Order Cellular Neural Networks”,

TÀI LIỆU THAM KHẢO

[1] Aein M. J., Talebi H.Ạ (2009), “Introducing a Training Methodology for Cellular Neural Networks with Application to Mechanical Vibration Problem”, IEEE Multi-conference on Systems and Control Saint Petersburg, Russia, pp. 1661- 1666.

[2] Arslan Ẹ, Orman Z. (2011), “Road Traffic Analysis on the CNN Universal Machine”, Proceedings of the World Congress on Engineering and Computer Science, 2011 (I), pp. 19-21.

[3] Aziz W., Controllability T. L. (2005), “Applications, and Numerical Simulations of Cellular Neural Networks”, Electronic Journal of Differential Equations, Conference (13), pp. 1-11.

[4] Ban J. C., Chang C. H., Lin S. S. (2012), “On the Structure of Multi-layer Cellular Neural Networks”, J -C. Ban et al. / J. Differential Equations (252), pp. 4563– 4597.

[5] Benziadị F., Kendouci Ạ (2016), “The Application of Kolmogorov’s Theorem in the one-Default Model”, Mathematical Sciences and Applications, pp. 71-78. [6] Bhambhani V., Herbert., Tanner G. (2010), “Topology Optimization in Cellular

Neural Networks”, Proceedings of the 49th IEEE Conference on Decision and Control, (15-17), pp. 3926-3931.

[7] Catherine D., Schuman., Thomas & James S. (2017), “A Survey of Neuromorphic Computing and Neural Networks in Hardware”, arXiv:1705.06963v1, (19), pp. 1-88.

[8] Cimagallị V., Balsị M. (1993), “Cellular Neural Network: A Review”,

Proceedings of Sixth Italian Workshop on Parallel Architectures and Neural Networks. Vietri sul Mare, Italy, pp. 12-14.

[9] Cuia B. T, Wuạ W. (2009), “Global Exponential Stability of High Order Recurrent Neural Network with Time-Varying Delays”. Applied Mathematical Modelling 33(1), pp. 198-210.

[10] Chen. Z., Meng. Z. (2012), “Exponential Convergence for Cellular Neural Networks with Time-Varying Delays in the Leakage Terms”, Abstract and Applied Analysis (2012), p. 1-10.

[11] Chua L. Ọ, Yang. (1988), “Cellular Neural Network Theory”, IEEE, Transactions on Circuits and Systems (35), p. 1259 - 1266.

[12] Elangọ P., Murugesan. K. (2009), “Digital Image Inpainting Using Cellular Neural Network”. Int. J. Open Problems Compt. Math, (2),pp. 339-350. [13] Elias. B., Kosmatopoulos., Marios. M., Polycarpoụ (1995), “High-Order Neural

Network Structures For Identification of Dynamical Systems”, IEEE Transactions on Neural Networks, 6(2), p. 422 – 431.

[14] Ettaouil. M., Elmoutaouakil. K., Ghanoụ Ỵ (2015), “The Continuous Hopfield Networks (CHN) for the Placement of the Electronic Circuit”, Weseas Wseas Transaction on Computers Joudar Nour-Eđine, El Moutouakil Karim, Ettaouil Mohamed, (14), pp. 1865-1874.

[15] Fantaccị R., Gubellinị R., Pecorellạ T., and Tarchị D. (2003), “A Cellular Neural Network Based Diffserv Switch for Satellite Communication Systems”,

Dipartimento di Elettronica e Telecomunicazioni Universit`a di Firenze Via di Santa Marta, 3 50139 Firenze - Italy, pp. 47-53.

[16] Fedotova Ạ V., Tarasov V. B., Alexeỵ, Averkin.N. (2016) “Time Series Prediction based on Hybrid Neural Networks”, Article in Science and Education of the Bauman MSTU, pp. 233-246.

[17] Gacsádị Ạ, Gravạ C., Straciuc. Ọ, Gavriluţ. Ị (2011), “PDE-Based Medical Images Denoising Using Cellular Neural Networks”, Proceedings of the 15th WSEAS International Conference on Systems, pp. 190-195.

[18] GacsádịẠ, GravạC., GravạA (2005), “Medical Image Enhancement by using Cellular Neural Networks”, Computers in Cardiology, IEEE/ Computers in Cardiology, pp. 821−824.

[19] Gaọ Q., Georgẹ, Moschytz. S. (2001), “Fingerprint Feature Extraction Using CNN”, European Conference on Circuit Theory and Design, pp. 28-31

[20] Goraş L. (2009), “Spatio-Temporal Dynamics in Cellular Neural Networks”. The Annals of “Dunarea De Jos” University of Galati Fascicle III, (32), pp. 5-10 [21] GuKzelis C., Karamamut. S., Genc. Ị (1998), “A Recurrent Perceptron Learning

Algorithm for Cellular Neural Networks”, An International Journal for Physical and Engineering Sciences volume (51), pp. 296–309.

[22] Guzelis. C., Chua L. Ọ (1993), “Stability Analysis of Generalized Cellular Neural Networks”, International Journal of Circuit Theory and Applications, (1), pp. 1-33.

[23] Haibo Gụ, Jang. H., Teng. Z. (2011), “On the Dynamics in High-Order Cellular Neural Networks with Time-Varying Delays”, Differential Equations and Dynamical Systems, (19), pp. 119-132.

[24] Hoan N. Q. (1996), “Mở rộng cấu trúc và hàm Lyapunov cho mạng nơron Hopfield”, Tạp chí Tin học và điều khiển học, 12(4), pp. 45-55.

[25] Horváth. Ạ, Hillmer. M., Qiuwen L. X., Hụ S., & Niemier. M. (2017), “Cellular Neural Network Friendly Convolutional Neural Networks-CNN with CNN”,

Design, Automation and Test in Europe, pp. 145-150.

[26] Hoụ Z., Zhụ H., Feng. C. H. (2013), “Existence and Global Uniform Asymptotic Stability of Almost Periodic Solutions for Cellular Neural Networks with Discrete and Distributed Delays”, Journal of Applied Mathematics, pp. 1-6.

[27] Huang. C., Kuang. H., Chen. X., Wen. F (2013), “An LMI Approach for Dynamics of Switched Cellular Neural Networks with Mixed Delays”,

Abstract and Applied Analysis, pp. 1-8.

[28] Huang Ỵ S., Wu C. W. (2005), “Stability of Cellular Neural Network with Small Delays”, Discrete and Continuous Dynamical Systems. Supplement (25), pp. 420–426.

[29] Huang. Z, Peng. L., Xụ M. (2010), “Anti-periodic Solutions for High-Cellula Neural Networks with Time-varying Delays”, Electronic Journal of Differential Equations, (59), pp. 1-9.

[30] Itoh. M., Chua L. Ọ (2004), “Star Cellular Neural Networks for Associative and Dynamic Memories”, International Journal of Bifurcation and Chaos, 14(5), pp. 1725–1772.

[31] Jankovic. M., Martinez. P., Chen. Z., Cichockị (2008), “Modified Modulated Hebb-Oja Learning Rule: A Method for Biologically Plausible Principal Component Analysis”, International Conference on Neural Information Processing, pp. 527–536.

[32] Jian. Ỵ, Pan. T., Shị B. (2012), “Global Stability of Almost Periodic Solution of a Class of Neutral-Type BAM Neural Networks”, Abstract and Applied Analysis, (1), pp. 1-18.

[33] Jung-C. B., Chih-H. C. (2013), “The layer Effect on Multi-layer Cellular Neural Networks”, Applied Mathematics Letters, 26(7), pp. 706-709.

[34] Katọ Ỵ, Uedạ Ỵ, Uwatẹ Ỵ, Nishiọ Ỵ (2011), “Cellular Neural Networks with Switching Two Types of Templates”, International Joint Conference on Neural Networks, pp. 1-25.

[35] Kawaguchị M., Ishiị N., Umenọ M. (2015), “Analog Neural Circuit and Hardware Design of Deep Learning Model”, Procedia Computer Science, (60), pp. 976-985.

[36] Koji´c. N., Reljin. Ị, Reljin. B. (2006), “Neural Network for Optimization of Routing in Communication Networks”, Facta Universitatis - series: Electronics and Energetics, (19), pp. 317-329

[37] Kuang. H., Liụ J., Chen. X, & Hẹ L. (2013), “Asymptotic Behavior of Switched Stochastic Delayed Cellular Neural Networks via Average Dwell Time Method” Abstract and Applied Analysis, pp. 1-9.

[38] Laị X. H., Yaọ T. X. (2013), “Exponential Stability of Impulsive Delayed Reaction-Diffusion Cellular Neural Networks via Poincaré Integral Inequality”,

Abstract and Applied Analysis, pp. 1-10.

[39] Laị X. H., Zhang. Ỵ (2012). “Fixed Point and Asymptotic Analysis of Cellular Neural Networks”, Abstract and Applied Analysis, pp. 1-10.

[40] Lị X. (2014), “Existence and Exponential Stability of Solutions for Stochastic Cellular Neural Networks with Piecewise Constant Argument”, Journal of Applied Mathematics, pp. 1-11.

[41] Lị Ỵ, Sun. L., Yang L. (2014), “Existence and Exponential Stability of Equilibrium Point for Fuzzy BAM Neural Networks with Infinitely Distributed Delays and Impulses on Time Scales”, Journal of Applied Mathematics, pp. 1- 17.

[42] Lị Ỵ, Wang. L., Feị Ỵ (2014), “Periodic Solutions for Shunting Inhibitory Cellular Neural Networks of Neutral Type with Time-Varying Delays in the Leakage Term on Time Scales”, Journal of Applied Mathematics, pp.1-16. [43] Lị Ỵ, Shen. S, “Almost Periodic Solutions of Clifford-Valued Fuzzy Cellular

Neural Networks with Time-Varying Delays” Neural Processing Letters, (51), pp. 1749-1769.

[44] Lị Ỵ, Xiang. J. (2019), “Global Asymptotic Almost Periodic Synchronization of Clifford-Valued CNN with Discrete Delays”, Complexity, pp. 1-13.

[45] Lị Ỵ, Xụ X., Yuan. C. (2020), “Enhanced Mask R-CNN for Chinese Food Image Detectio”, Journal of Applied Mathematics, pp. 1-8.

[46] Lị Ỵ, Zhaọ L., Yang. L. (2015), “Almost Periodic Solutions of BAM Neural network with Time-Varying Delays on Time Scales”, Scientific World Journal, pp. 1-15.

[47] Lị Ỵ, Zhị Ỵ (2014), “Global Exponential Stability for DCNN with Impulses on Time Scales”, Mathematical Problems in Engineering, pp. 1-10.

[48] Liang J. Ỵ, Wu, P. X. (2012), “Study on Neural Networks in Parallel Computing Environments”, Applied Mechanics and Materials, pp. 707-710.

[49] Lin Ỵ L., Hsieh J. G., Jeng J. H. (2013), “Robust Template Decomposition without Weight Restriction for Cellular Neural Networks Implementing Arbitrary Boolean Functions Using Support Vector Classifiers”, Mathematical Problems in Engineering, pp. 1-9.

[50] Liu J. B., Razạ Z., Javaid. M. (2020), “Zagreb Connection Numbers for Cellular Neural Networks”, Discrete Dynamics in Nature and Society, pp. 1-8.

[51] Long P. Đ., Cat P. T (2006), “Công nghệ mạng nơron tế bào - CNN và ứng dụng”, Tạp chí Tin học và Điều khiển học, 22(1), pp. 37-44.

[52] Lou Q. W., Pan. C., Mcguinness. J, Horvath. A, Naeemị Ạ (2016), “A Mixed Signal Architecture for Convolutional Neural Networks”, ACM Journal on Emerging Technologies in Computing Systems, 1(1), pp. 1-25.

[53] Máriọ P., Véstias. (2019), “A Survey of Convolutional Neural Networks on Edge with Reconfigurable Computing”, Algorithms 2019, pp. 1-24.

[54] Mateị R., Grigoras. C. (2008), “Nonlinear Dynamics in CNN with Second Order Cells”. IEEE Xplore: 05 Aug 2008, pp. 124-129.

[55] Meị Xuehuị, Xing. J., & Jiang. H. (2013), “Adaptive Synchronization for a Class of Cellular Neural Networks with Pantograph Delays”, Abstract and Applied Analysis, pp. 1-7.

[56] Mohammadi S. K., Jassbị J., Makvandị P. (2005), “Application of Genetic Algorithm and Neural Network in Forecasting with Good Data”, Proceedings of the 6th Wseas Int. Conf. on Neural Network, Lisbon, Portugal, pp. 56-61. [57] Mohd-Idrus. M. Ị, Katọ Ỵ (2012), “Research on a New Structure of Three-

Layer Cellular Neural Networks”, IEEE Workshop on Nonlinear Circuit Netwo Partial Derivatives, pp. 109-110.

[58] Negnevitskỵ M. (2005), “Artificial Intelligence: A Guide to Intelligent Systems”. Pearson Education Limited, Edinburgh Gate, Harlow, Essex CM20 2JE, England, Seconds edition published, (196), 2005.

[59] Ojhạ Ạ K., Mallick. D. (2007), “Logarithmic Stability of Neural Networks with Time-Varying Delay”, International Journal of Computational and Applied Mathematics, 2(3), pp. 209–219.

[60] Piccininị G (2004), “The First Computational Theory of Mind and Brain: A Close Look at Mcculloch and Pitts's”, An International Journal for Epistemology, Methodology and Philosophy of Science (141), pp. 175–215. [61] Phương D. T., Cat P. T (2013), “Đồng bộ thích nghi mạng CNN hỗn loạn và

ứng dụng trong bảo mật truyền thông”, Tạp chí Tin học và Điều khiển học,

[62] Razạ Z., Liụ J. B., Javaid. H. (2020), “Zagreb Connection Numbers for Cellular Neural Networks”, Discrete Dynamics in Nature and Society, pp. 1-8.

[63] Ren. Ỵ, Lị Ỵ (2012), “Stability and Existence of Periodic Solutions for Cellular Neural Networks with State Dependent Delays on Time Scales”, Discrete Dynamics in Nature and Society, pp. 1-14.

[64] Roskạ T., Chua L. Ọ (1993), “the CNN Universal Machine: An Analogic Array Computer”, IEEẸ Trans. Circuits and Systems-II, Analog and Digital Signal Processing, 40(3), pp. 163-173.

[65] Sahin. S., Beceriklị Ỵ, Yazicị S. (2006), “Neural Network Implementation in Hardware Using FPGAs”, ICONIP 2006, Part III, LNCS 4234, pp. 1105-1112. [66] Slavovạ A (2003), “Cellular Neural Networks: Dynamics and odelling”,

Springer Science and Business Media Dordrecht, (16), pp 22-28.

[67] Tan. M., Xụ S., Lị Z. (2015), “Dynamics of High Order Fuzzy Cellular Neural Networks with Time-Varying Delays”, International Journal of Computational Intelligence Systems, 8(2), pp. 381-394.

[68] Tokes. S., Orzọ L., Ayoub. Ạ (2006), “Programmable OASLM as a Novel Sensing Cellular Computer” IEEE International Workshop on Cellular Nanoscale Networks and Their Applications, (2006), pp. 1-5.

[69] Tùng C. T., Cat P. T. (2010), “Xử lý ảnh Y tế 4D-CT chịu nén sử dụng mạng nơron tế bào”, Tạp chí Tin học và Điều khiển học, 26(4), pp. 351-360

[70] Thanh D. P., Cat P. T. (2015), “Adaptive Synchronization of Chaotic SC-CNN with Uncertain State Template”, Mathematical Problems in Engineering, Mathematical Problems in Engineering, (2015), pp. 1-10.

[71] Vagliasindị G., Murarị Ạ, & EFDẠ J. (2006), “Application of Cellular Neural Network Methods to Real Time Adaptability Analysis in Plasma Fusion”, Proc. 21 st IAEA Fusion Energy Conference, pp. 1-11.

[72] Vries. B. Dẹ, Josẹ, Principẹ C., Oliveirạ P (2012), “Adaline with adaptive Plasticidad Cerebral y Hábito en William James: un Antecedente para la Neurociencia Social”, Psychologia Latina, 3(1), pp. 1-9.

[73] Wang. W., Liụ B. (2014), “Global Exponential Stability of Pseudo Almost Periodic Solutions for SICNN with Time-Varying Leakage Delays”, Abstract and Applied Analysis, pp1-17.

[74] Wang.Ỵ, Zhang. Z., Cuị J. (2007), “The Architecture and Circuital Implementation Scheme of a New Cell Neural Network for Analog Signal Processing”, Journal of Universal Computer Science, 13(9), pp. 1344-1353. [75] Wụ H. (2011), “Pseudo Almost-Periodic Solution of Shunting Inhibitory

Cellular Neural Networks with Delay”, Journal of Applied Mathematics, pp. 1- 14.

[76] Wụ W. (2014), “Global Exponential Stability of a Unique Almost Periodic Solution for Neutral-Type Cellular Neural Networks with Distributed Delays”,

Journal of Applied Mathematics, pp. 1-8.

[77] Xiong. W. (2015), “New Result on Convergence for HCNN with time-Varying Leakage Delays” Neural Computing and Applications, (26), pp. 485-491. [78] Yang. G., Kaọ Ỵ, Wang. C. (2013), “Exponential Stability and Periodicity of

Fuzzy Delayed Reaction-Diffusion Cellular Neural Networks with Impulsive Effect”, Research Article Abstract and Applied Analysis, pp. 1-9.

[79] Yang. X., Song. Q., Liụ Ỵ, Zhaọ Z. (2014), “Global Asymptotic Stability of Impulsive CNN with Proportional Delays and Partially Lipschitz Activation Functions”, Abstract and Applied Analysis, pp. 1-11.

[80] Yaọ T., Laị X. (2014), “Mean-Square Exponential Stability Analysis of Stochastic Neural Networks with Time-Varying Delays via Fixed”, Journal of Applied Mathematics, pp. 1-9.

[81] Yu X. Z., Yuan. R., Hsu C. H., Peng M. S. (2014), “Traveling Waves for Delayed Cellular Neural Networks with Non Monotonic Output Functions”, Abstract and Applied Analysis, pp. 1-11.

[82] Yu Ỵ H. (2016), “Global Exponential Convergence for a Class of HCNN with Neutral time-proportional Delays”, Applied Mathematics and Computation

(285), pp. 1-7.

[83] Zarándỵ Á., Horváth. Ạ, Szolgaỵ P. (2018), “CNN Technology-Tools and Applications”, IEEE Circuits and Systems Magazine, (18), pp. 77 - 89.

[84] Zeng. Z., Wang. J. (2009), “Analysis and Design of Associative Memories Based On Cellular Neural Networks with Space-invariant Cloning Templates”

Proceedings of International Joint Conference on Neural Networks, Atlanta, Georgia, USA, Jun, pp. 14-19.

[85] Zhang. H., Yang. M. (2013), “Global Exponential Stability of Almost Periodic Solutions for SICNN with Continuously Distributed Leakage Delays”, Abstract and Applied Analysis, pp. 1-14.

[86] Zhang. J. (2007), “Kohonen Self-Organizing Map–An Artificial Neural Network” Visualization for Information Retrieval, pp. 107-125.

[87] Zhang. Q., Weị X., Xụ J. (2008), “Convergence of Discrete-Time Cellular Neural Networks with Time-Varying Delays”, International Journal of Innovative Computing, Information and Control, 4(11), pp. 2997-3004. [88] Zhang. Ỵ, Guan. Ỵ (2013), “Asymptotic Stability of Impulsive Cellular Neural

Networks with Infinite Delays via Fixed Point Theory”, Abstract and Applied Analysis, pp. 1-10.

[89] Zhụ L., Ikedạ K., Pang. P., Zhang. R., Sarrafzadeh. Ạ (2016), “A Brief Review of Spin-Glass Applications in Unsupervised and Semi-Supervised Learning”,

PHỤ LỤC 1

CHỨNG MINH CÁC ĐỊNH LÝ CỦA MẠNG NƠRON TẾ BÀO [11]

Trước khi thiết kế một CNN vật lý, việc đầu tiên cần phải biết phạm vi động của mạng để đảm bảo rằng mạng sẽ thỏa mãn các giả định về các phương trình động học, yêu cầu đặt ra phải thỏa mãn các điều kiện được trình bày trong (1.33) của chương 1. Để đảm bảo nền tảng cho việc thiết kế mạng nơron tế bào, tác giả tiến hành xem xét các định lý trong [11], như saụ

Định lý 1

Định lý được Leon Ọ Chua phát biểu [11]. Tất cả các trạng thái xij trong CNN đều bị giới hạn với mọi thời gian t > 0 và điều kiện ràng buộc liên kết vmax được tính theo công thức sau cho các mạng nơron tế bào (1.37).

( ) x ( , ) ( , ) max 1 ( , ; , ) ( , ; , ) ma i j x x k l vR I R A i j k l B i j k l      = + +  + (P1.1) Chứng minh

Để chứng minh, ta viết lại phương trình động động học của tế bào như sau:

( ) 1 ' ( ) ( ) ( ) ij ij ij ij x dx t x t f t g u I dt = −R C + + + 1 i M 1 j N (P1.2a) trong đó: ( , ) 1 ( ) ( , ; , ) ( ) ij k l kl f t A i j k l y t C =  1 i M 1 j N (P1.2b) ( , ) 1 ( ) ( , ; , ) ij kl k l g u B i j k l u C =  1 i M 1 j N (P1.2c) ' I I C = (P1.2d)

Cho 1 ( ) ij MN U E t

 trong ma trận MN chiều có phương trình vectơ đầu vào không đổi (P1.2a) là phương trình bậc nhất và nó được cho bởi:

( ) (0) t R Cx ij ij x t x e − = + ( ) 0 ' ( ) ( ) ( ) ( ) t R Cx ij ij ij ij t e f h g u p u I d     − −       + + + + + (P1.3) Theo đó ta có: ( ) 0 ' ( ) (0) ( ) ( ) t t R Cx t R Cx ij ij ij ij x t x e e f g u I d    − − −        +  + + ( ) 0 ' (0) ( ) ( ) t t R Cx t R Cx ij ij ij x e e f g u I d    − − −        + + + ( ) 0 ' (0) t t R Cx t R Cx ij ij ij x e F G I e d   − − −  + +       +  xij(0) RxCFij +Gij + I'      + Ở đây: ( , ) 1 max ( ) ( , ; , ) max ( ) ij t ij k l t kl F f t A i j k l y t C =   (P1.4a) ( , ) 1 max ( ) ( , ; , ) max ij u ij u kl k l G g u B i j k l u C =   (P1.4b) Từ xij(0) và uij thỏa mãn các điều kiện trong trong (2d) và (2e) và yij( )t thỏa mãn điều kiện:

( ) 1

ij t

y  cho mọi thời gian t

Với đặc trưng được trình bày trong (2b) [11], tiếp theo là (P.3) và (P.4) ta có: xij( )txij(0) ( , ) ( , ; , ) max ( ) ( , ; , ) max x t kl u kl k l RA i j k l y t B i j k l u I    +  + + ( ) ( , ) 1 x ( , ; , ) ( , ; , ) k l I RA i j k l B i j k l  +      +  +

1 i M, 1 j N (P1.5) Dễ thấy: ( ) ( , ) ( , ) max 1 ( , ; , ) ( , ; , ) max x i j k l vR I Rx A i j k l B i j k l      = + +  + (P1.6)

Do vmax không phụ thuộc vào thời gian t và tế bào C( , )i j với mọi ij, ta có:

max ij

t

max xv 1 i M, 1 j N (P1.7) Với bất kỳ mạng nơron tế bào, các tham sốRx, C, I, ( , ; , )A i j k l , ( , ; , )B i j k l

Một phần của tài liệu Phát triển mạng nơron tế bào đa tương tác và khả năng ứng dụng (Trang 111 - 140)

Tải bản đầy đủ (PDF)

(140 trang)