Nonnegative periodic dynamics of cohen-grossberg neural networks with discontinuous activations and discrete time delays

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 5551 LNCS, Issue PART 1, 2009, Pages 579-588

  He, Xiangnan ^a   Lu, Wenlian ^a   Chen, Tianping ^a  

^a FUDAN UNIVERSITY   (China)

Author keywords

[No Author keywords available]

Indexed keywords

ACTIVATION FUNCTIONS; ASYMPTOTICAL STABILITY; CAUCHY PROBLEMS; COHEN-GROSSBERG NEURAL NETWORKS; DISCRETE TIME DELAY; EXTERNAL INPUT; NUMERICAL EXAMPLE; PERIODIC DYNAMICS; PERIODIC SOLUTION; THEORETICAL RESULT;

CHEMICAL ACTIVATION; UNMANNED AERIAL VEHICLES (UAV);

NEURAL NETWORKS;

EID: 69949088388     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/978-3-642-01507-6_66     Document Type: Conference Paper

References (35)

1. Cohen, M.A., Grossberg, S.: Absolute Stability and Global Pattern Formation and Parallel Storage by Competitive Neural Networks. IEEE Transactions on systems, Man, and Cybernectics 13, 815-826 (1983)
2. Hopfield, J.J., Tank, D.W.: Computing with Neural Circuits: a Model. Science 233, 625-633 (1986)
3. Hirsh, M.: Convergence Activation Dynamics in Continuous Time Networks. Neural Networks 2, 331-349 (1989)
4. Michel, A.N., Gray, D.L.: Analysis and Synthesis of Neural Networks with Lower Block Triangular Interconnecting Structure. IEEE Transactions on Circuits and System 37, 1267-1283 (1990)
5. Forti, M., Tesi, A.: New Condition for Global Stability of Neural Networks with Application to Linear Quadratic Programming Problems. IEEE Transactions on Circuits and Systems-1 42, 354-366 (1995)
6. Lu, W., Chen, T.P.: New Conditions Global Stability of Cohen-Grossberg Neural Networks. Neural Computation 15, 1173-1189 (2003)
7. Bleair, J., Campbell, S.A., Driessche, P.: Stability and Delay-Induced Oscillations in a Neural Network Model. SIAM. Appl. Math. 56, 245-255 (1996)
8. Cao, J., Zhou, D.: Stability Analysis of Delayed Neural Networks. Neural Networks 11, 1601-1605 (1998)
9. Chen, T.P.: Global Exponential Stability of Delayed Hopfield Neural Networks. Neural Networks 14, 977-980 (2001)
10. Civalleri, P.P., Gilli, L.M., Pabdolfi, L.: On Stability of Cellular Neural Networks with Delay. IEEE Transactions on Circuits and Systems 40, 157-164 (1993)
11. Gopalasamy, K., He, X.: Stability in Asymmetric Hopfield Nets with Transmission Delays. Phys. D 76, 344-358 (1991)
12. Joy, M.P.: Results Concerning the Absolute Stability of Delayed Neural Networks. Neural Networks 13, 613-616 (2000)
13. Lu, W., Rong, L., Chen, T.P.: Global Convergence of Delayed Neural Network Systems. International Journal of Neural Systems 13, 193-204 (2003)
14. Cao, J.: New Results Concerning Exponential Stability and Periodic Solutions of Delayed Cellular Neural Networks. Phys. Lett. A 307, 136-147 (2003)
15. Chen, T.P., Lu, W., Chen, G.: Dynamical Behaviors of a Large Class of General Delayed Neural Networks. Neural Computation 17, 949-968 (2005)
16. Gopalsamy, K.S.: Time Delays and Stimulus-Dependent Pattern Formation in Periodic Environments in Isolated Neurals. IEEE Transactions Neural Networks 13, 551-563 (2002)
17. Lu, W., Chen, T.P.: On Periodic Dynamical Systems. Chin. Ann. Math. 25B, 455-462 (2004)
18. Zhou, J., Liu, Z., Chen, G.: Dynamics of Delayed Periodic Neural Networks. Neural Networks 17, 87-101 (2004)
19. Zheng, Y., Chen, T.: Global Exponential Stability of Delayed Periodic Dynamical Systems. Phys. Lett. A 322, 344-355 (2004)
20. Huang, X., Cao, J.: Almost Periodic Solution of Shunting Inhibitory Cellular Neural Networks with Time-Varying Delays. Phys. Lett. A 314, 222-231 (2003)
21. Lu, W., Chen, T.P.: Global Exponential Stability of Almost Periodic Solutions for a Large Class Of Delayed Dynamical Systems. Sci. Chin. Ser. A MAth. 48, 1015-1026 (2005)
22. Wang, L., Zou, X.: Exponential Stability of Cohen-Grossberg Neural Networks. Neural Networks 15, 415-422 (2002) (Pubitemid 34518408)
23. Chen, T., Rong, L.: Robust Global Exponential Stability of Cohen-Grossberg Neural Networks with Time Delays. IEEE Trans. Neural Networks 15, 203-206 (2004)
24. Grossberg, S.: Biological Competition: Decision Rules, Pattern Formation, and Oscillations. Proceedings of the National Academy of Sciences of the United States of Amercia 77(4), 2338-2342 (1980)
25. Grossberg, S.: Nonlinear Neural Networks Principles, Mechanisms, and Architectures. Neural Networks 1, 17-66 (1988)
26. Lin, W., Chen, T.P.: Positive Periodic Solutions of Delayed Periodic Lotka-Volterra Systems. Phys. Lett. A 334, 273-287 (2005)
27. Lu, W., Chen, T.P.: Rn n-Global Stability of a Cohen-Grossberg Neural Network with Nonnegative Equilibria. Neural Networks 20, 714-722 (2007)
28. Forti, M., Nistri, P.: Global Convergence of Neural Networks with Discontinuous Neuron Activations. IEEE Trans. Circuits Syst.-1 50(11), 1412-1435 (2003)
29. Lu, W., Chen, T.P.: Dynamical Behavious of Cohen-Grossberg Neural Networks with Discontinuous Activation Functions. Neural Networks 18, 231-242 (2005)
30. Forti, M., Nistri, P., Papini, D.: Global Exponential Stability and Global Convergence in Finite Time of Delayed Neural Networks with Infinite Gain. IEEE Transactions on Neural Networks 16, 1449-1463 (2005)
31. Lu, W., Chen, T.P.: Dynamical Behaviors of Delayed Neural Network Systems with Discontinuous Activation Functions. Neural Computation 18, 683-708 (2006)
32. Papini, D., Taddei, V.: Global Exponential Stability of the Periodic Solution of the Delayed Neural Networks with Discontinuous Activations. Phys. Lett. A 343, 117-128 (2005)
33. Lu, W., Chen, T.P.: Almost Periodic Dynamics of a Class Of Delayed Neural Networks with Discontinuous Activations. Neural Computation 20, 1065-1090 (2008)
34. Filippov, A.F.: Differential Equations with Discontinuous Right-Hand Sides. Mathematics and Its Applications (Soviet Series). Kluwer Academic Publishers, Boston (1988)
35. Aubin, J.P., Frankowska, H.: Set-Valued Analysis. Birkhäusera, Boston (1990)