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A weak condition for global stability of delayed neural networks
1. | School of Computer and Information Engineering, Hechi University, Guangxi, Yizhou 546300, China |
2. | Department of Mathematics and Statistics, Curtin University of Technology, Perth, WA 6845 |
3. | School of Mathematics and Statistics, Hechi University, Guangxi, Yizhou 546300, China |
4. | Department of Mathematics and Statistics, Curtin University, Perth,WA 6845, Australia |
5. | School of Information Science and Engineering, Central South University, Changsha, Hunan 410083, China |
References:
[1] |
S. Abe, J. Kawakami and K. Hirasawa, Solving inequality constrained combinatorial optimization problems by the hopfield neural networks, Neural Networks, 5 (1992), 663-670.
doi: 10.1016/S0893-6080(05)80043-7. |
[2] |
P. Baldi and A. F. Atiya, How delays affect neural dynamics and learning, IEEE Transactions on Neural Networks, 5 (1994), 612-621.
doi: 10.1109/72.298231. |
[3] |
D. Calabuig, J. F. Monserrat, D. Gmez-Barquero and O. Lzaro, An efficient dynamic resource allocation algorithm for packet-switched communication networks based on Hopfield neural excitation method, Neurocomputing, 71 (2008), 3439-3446. |
[4] |
Y. Chen and H. Xu, Exponential stability analysis and impulsive tracking control of uncertain time-delayed systems, Journal of Global Optimization, 52 (2012), 323-334.
doi: 10.1007/s10898-011-9669-2. |
[5] |
M. Forti, On global asymptotic stability of a class of nonlinear systems arising in neural network theory, J. Differential Equations, 113 (1994), 246-264.
doi: 10.1006/jdeq.1994.1123. |
[6] |
M. Forti, S. Maneti and M. Marini, Necessary and sufficient conditions for absolute stability of neural networks, IEEE Trans. Circuits Syst. I, 41 (1994), 491-494.
doi: 10.1109/81.298364. |
[7] |
M. Forti and A. Tesi, New conditions for global stability of neural networks with application to linear and quadratic programming problems, IEEE Trans. Circuits Syst. I, 42 (1995) 354-366.
doi: 10.1109/81.401145. |
[8] |
A. Gasull, J. Llibre and J. Sotomayor, Global asymptotic stability of differential equations in the plane, J. Differential Equations, 91 (1991) 327-336.
doi: 10.1016/0022-0396(91)90143-W. |
[9] |
K. Gopalsamy and X. He, Stability in asymmetric Hopfield nets with transmission delays, Physica D, 76 (1994), 344-358.
doi: 10.1016/0167-2789(94)90043-4. |
[10] |
M. W. Hirsch, Convergent activation dynamics in continuous time networks, Neural Netw., 2 (1989), 331-349.
doi: 10.1016/0893-6080(89)90018-X. |
[11] |
J. J. Hopfield, Neurons with graded response have collective computational properties like those of two-state neurons, Proc. Aead. Sci. USA, 81 (1984), 3088-3092.
doi: 10.1073/pnas.81.10.3088. |
[12] |
A. O. Ignatyev, On the stability of equilibrium for almost periodic systems, Nonlinear Anal., 29 (1997), 957-962.
doi: 10.1016/S0362-546X(96)00078-8. |
[13] |
E. Kaszkurewicz and A. Bhaya, On a class of globally stable neural circuits, IEEE Trans. Circuits Syst. I, 41 (1994), 171-174.
doi: 10.1109/81.269055. |
[14] |
D. G. Kelly, Stability in contractive nonlinear neural networks, IEEE Trans. Biomed. Eng., 3 (1990), 231-242.
doi: 10.1109/10.52325. |
[15] |
N. Laskaris, S. Fotopoulos, P. Papathanasopoulos and A. Bezerianos, Robust moving averages, with Hopfield neural network implementation, for monitoring evoked potential signals, Electroencephalography and Clinical Neurophysiology/ Evoked Potentials Section, 104 (1997), 151-156.
doi: 10.1016/S0168-5597(97)96681-8. |
[16] |
X. Liao, G. Chen and E. N. Sanchez, Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach, Neural Networks, 15 (2002), 855-866 |
[17] |
X. Liu and T. Chen, A new result on the global convergence of Hopfield neural networks, IEEE Trans. Circuits Syst. I, 49 (2002), 1514-1516.
doi: 10.1109/TCSI.2002.803358. |
[18] |
C. Marcus and R. Westervelt, Stability of analog neural networks with delay, Phys. Rev. A, 39 (1989), 347-359.
doi: 10.1103/PhysRevA.39.347. |
[19] |
A. N. Markus and H. Yamabe, Global stability criteria for differential systems, Osaka Math. J., 12 (1960), 305-317. |
[20] |
Z. Orman, New sufficient conditions for global stability of neutral-type neural networks with time delays, Neurocomputing, 97 (2012), 141-148.
doi: 10.1016/j.neucom.2012.05.016. |
[21] |
S. Rout, Seethalakshmy, P. Srivastava and J. Majumdar, Multi-modal image segmentation using a modified Hopfield neural network, Pattern Recognition, 31 (1998), 743-750.
doi: 10.1016/S0031-3203(97)00089-7. |
[22] |
R. Sammouda, N. Adgaba, A. Touir and A. Al-Ghamdi, Agriculture satellite image segmentation using a modified artificial Hopfield neural network, Computers in Human Behavior, 30 (2014), 436-441.
doi: 10.1016/j.chb.2013.06.025. |
[23] |
P. Suganthan, E. Teoh and D. Mital, Pattern recognition by homomorphic graph matching using Hopfield neural networks, Image and Vision Computing, 13 (1995), 45-60.
doi: 10.1016/0262-8856(95)91467-R. |
[24] |
H. Tamura, Z. Zhang, X. S. Xu, M. Ishii and Z. Tang, Lagrangian object relaxation neural network for combinatorial optimization problems, Neurocomputing, 68 (2005), 297-305.
doi: 10.1016/j.neucom.2005.03.003. |
[25] |
W. Walter, Analysis I, second ed., Springer-Verlag, Berlin, 1990. |
[26] |
R. L. Wang, Z. Tang and Q. P. Cao, A lear ning method in Hopfield neural network for combinatorial optimization problem, Neurocomputing, 48 (2002), 1021-1024. |
[27] |
H. Wersing, W. J. Beyn and H. Ritter, Dynamical stability conditions for recurrent neural networks with unsaturating piecewise linear transfer functions, Neural Comput., 13 (2001), 1811-1825.
doi: 10.1162/08997660152469350. |
[28] |
J. Wu, Symmetric functional-differential equations and neural networks with memory, Trans. Am. Math. Soc., 350 (1999), 4799-4838.
doi: 10.1090/S0002-9947-98-02083-2. |
[29] |
J. Wu and X. Zou, Patterns of sustained oscillations in neural networks with time delayed interactions, Appl. Math. Comput., 73 (1995), 55-75.
doi: 10.1016/0096-3003(94)00203-G. |
[30] |
H. Xu and Y. Chen and K. L. Teo, Global exponential stability of impulsive discrete-time neural networks with time-varying delays, Applied Mathematics and Computations, 217 (2010), 537-544.
doi: 10.1016/j.amc.2010.05.087. |
[31] |
H. Xu and K. L. Teo, $H_\infty$ optimal stabilization of a class of uncertain impulsive systems: an LMI approach, Journal of Industrial and management optimization, 5 (2009), 153-159.
doi: 10.3934/jimo.2009.5.153. |
[32] |
F. Zhang, The Schur complement and its applications. Numerical Methods and Algorithms, New York: Springer-Verlag, 4 (2005), 34.
doi: 10.1007/b105056. |
[33] |
W. Zhang, A weak condition of globally asymptotic stability for neural networks, Applied Mathematics Letters, 19 (2006), 1210-1215.
doi: 10.1016/j.aml.2006.01.009. |
[34] |
show all references
References:
[1] |
S. Abe, J. Kawakami and K. Hirasawa, Solving inequality constrained combinatorial optimization problems by the hopfield neural networks, Neural Networks, 5 (1992), 663-670.
doi: 10.1016/S0893-6080(05)80043-7. |
[2] |
P. Baldi and A. F. Atiya, How delays affect neural dynamics and learning, IEEE Transactions on Neural Networks, 5 (1994), 612-621.
doi: 10.1109/72.298231. |
[3] |
D. Calabuig, J. F. Monserrat, D. Gmez-Barquero and O. Lzaro, An efficient dynamic resource allocation algorithm for packet-switched communication networks based on Hopfield neural excitation method, Neurocomputing, 71 (2008), 3439-3446. |
[4] |
Y. Chen and H. Xu, Exponential stability analysis and impulsive tracking control of uncertain time-delayed systems, Journal of Global Optimization, 52 (2012), 323-334.
doi: 10.1007/s10898-011-9669-2. |
[5] |
M. Forti, On global asymptotic stability of a class of nonlinear systems arising in neural network theory, J. Differential Equations, 113 (1994), 246-264.
doi: 10.1006/jdeq.1994.1123. |
[6] |
M. Forti, S. Maneti and M. Marini, Necessary and sufficient conditions for absolute stability of neural networks, IEEE Trans. Circuits Syst. I, 41 (1994), 491-494.
doi: 10.1109/81.298364. |
[7] |
M. Forti and A. Tesi, New conditions for global stability of neural networks with application to linear and quadratic programming problems, IEEE Trans. Circuits Syst. I, 42 (1995) 354-366.
doi: 10.1109/81.401145. |
[8] |
A. Gasull, J. Llibre and J. Sotomayor, Global asymptotic stability of differential equations in the plane, J. Differential Equations, 91 (1991) 327-336.
doi: 10.1016/0022-0396(91)90143-W. |
[9] |
K. Gopalsamy and X. He, Stability in asymmetric Hopfield nets with transmission delays, Physica D, 76 (1994), 344-358.
doi: 10.1016/0167-2789(94)90043-4. |
[10] |
M. W. Hirsch, Convergent activation dynamics in continuous time networks, Neural Netw., 2 (1989), 331-349.
doi: 10.1016/0893-6080(89)90018-X. |
[11] |
J. J. Hopfield, Neurons with graded response have collective computational properties like those of two-state neurons, Proc. Aead. Sci. USA, 81 (1984), 3088-3092.
doi: 10.1073/pnas.81.10.3088. |
[12] |
A. O. Ignatyev, On the stability of equilibrium for almost periodic systems, Nonlinear Anal., 29 (1997), 957-962.
doi: 10.1016/S0362-546X(96)00078-8. |
[13] |
E. Kaszkurewicz and A. Bhaya, On a class of globally stable neural circuits, IEEE Trans. Circuits Syst. I, 41 (1994), 171-174.
doi: 10.1109/81.269055. |
[14] |
D. G. Kelly, Stability in contractive nonlinear neural networks, IEEE Trans. Biomed. Eng., 3 (1990), 231-242.
doi: 10.1109/10.52325. |
[15] |
N. Laskaris, S. Fotopoulos, P. Papathanasopoulos and A. Bezerianos, Robust moving averages, with Hopfield neural network implementation, for monitoring evoked potential signals, Electroencephalography and Clinical Neurophysiology/ Evoked Potentials Section, 104 (1997), 151-156.
doi: 10.1016/S0168-5597(97)96681-8. |
[16] |
X. Liao, G. Chen and E. N. Sanchez, Delay-dependent exponential stability analysis of delayed neural networks: an LMI approach, Neural Networks, 15 (2002), 855-866 |
[17] |
X. Liu and T. Chen, A new result on the global convergence of Hopfield neural networks, IEEE Trans. Circuits Syst. I, 49 (2002), 1514-1516.
doi: 10.1109/TCSI.2002.803358. |
[18] |
C. Marcus and R. Westervelt, Stability of analog neural networks with delay, Phys. Rev. A, 39 (1989), 347-359.
doi: 10.1103/PhysRevA.39.347. |
[19] |
A. N. Markus and H. Yamabe, Global stability criteria for differential systems, Osaka Math. J., 12 (1960), 305-317. |
[20] |
Z. Orman, New sufficient conditions for global stability of neutral-type neural networks with time delays, Neurocomputing, 97 (2012), 141-148.
doi: 10.1016/j.neucom.2012.05.016. |
[21] |
S. Rout, Seethalakshmy, P. Srivastava and J. Majumdar, Multi-modal image segmentation using a modified Hopfield neural network, Pattern Recognition, 31 (1998), 743-750.
doi: 10.1016/S0031-3203(97)00089-7. |
[22] |
R. Sammouda, N. Adgaba, A. Touir and A. Al-Ghamdi, Agriculture satellite image segmentation using a modified artificial Hopfield neural network, Computers in Human Behavior, 30 (2014), 436-441.
doi: 10.1016/j.chb.2013.06.025. |
[23] |
P. Suganthan, E. Teoh and D. Mital, Pattern recognition by homomorphic graph matching using Hopfield neural networks, Image and Vision Computing, 13 (1995), 45-60.
doi: 10.1016/0262-8856(95)91467-R. |
[24] |
H. Tamura, Z. Zhang, X. S. Xu, M. Ishii and Z. Tang, Lagrangian object relaxation neural network for combinatorial optimization problems, Neurocomputing, 68 (2005), 297-305.
doi: 10.1016/j.neucom.2005.03.003. |
[25] |
W. Walter, Analysis I, second ed., Springer-Verlag, Berlin, 1990. |
[26] |
R. L. Wang, Z. Tang and Q. P. Cao, A lear ning method in Hopfield neural network for combinatorial optimization problem, Neurocomputing, 48 (2002), 1021-1024. |
[27] |
H. Wersing, W. J. Beyn and H. Ritter, Dynamical stability conditions for recurrent neural networks with unsaturating piecewise linear transfer functions, Neural Comput., 13 (2001), 1811-1825.
doi: 10.1162/08997660152469350. |
[28] |
J. Wu, Symmetric functional-differential equations and neural networks with memory, Trans. Am. Math. Soc., 350 (1999), 4799-4838.
doi: 10.1090/S0002-9947-98-02083-2. |
[29] |
J. Wu and X. Zou, Patterns of sustained oscillations in neural networks with time delayed interactions, Appl. Math. Comput., 73 (1995), 55-75.
doi: 10.1016/0096-3003(94)00203-G. |
[30] |
H. Xu and Y. Chen and K. L. Teo, Global exponential stability of impulsive discrete-time neural networks with time-varying delays, Applied Mathematics and Computations, 217 (2010), 537-544.
doi: 10.1016/j.amc.2010.05.087. |
[31] |
H. Xu and K. L. Teo, $H_\infty$ optimal stabilization of a class of uncertain impulsive systems: an LMI approach, Journal of Industrial and management optimization, 5 (2009), 153-159.
doi: 10.3934/jimo.2009.5.153. |
[32] |
F. Zhang, The Schur complement and its applications. Numerical Methods and Algorithms, New York: Springer-Verlag, 4 (2005), 34.
doi: 10.1007/b105056. |
[33] |
W. Zhang, A weak condition of globally asymptotic stability for neural networks, Applied Mathematics Letters, 19 (2006), 1210-1215.
doi: 10.1016/j.aml.2006.01.009. |
[34] |
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