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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.
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.
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. Google Scholar |
[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.
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.
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.
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.
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.
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.
doi: 10.1016/0167-2789(94)90043-4. |
[10] |
M. W. Hirsch, Convergent activation dynamics in continuous time networks,, Neural Netw., 2 (1989), 331.
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.
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.
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.
doi: 10.1109/81.269055. |
[14] |
D. G. Kelly, Stability in contractive nonlinear neural networks,, IEEE Trans. Biomed. Eng., 3 (1990), 231.
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.
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. Google Scholar |
[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.
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.
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.
|
[20] |
Z. Orman, New sufficient conditions for global stability of neutral-type neural networks with time delays,, Neurocomputing, 97 (2012), 141.
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.
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.
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.
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.
doi: 10.1016/j.neucom.2005.03.003. |
[25] |
W. Walter, Analysis I,, second ed., (1990). Google Scholar |
[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. Google Scholar |
[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.
doi: 10.1162/08997660152469350. |
[28] |
J. Wu, Symmetric functional-differential equations and neural networks with memory,, Trans. Am. Math. Soc., 350 (1999), 4799.
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.
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.
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.
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).
doi: 10.1007/b105056. |
[33] |
W. Zhang, A weak condition of globally asymptotic stability for neural networks,, Applied Mathematics Letters, 19 (2006), 1210.
doi: 10.1016/j.aml.2006.01.009. |
[34] |
Available from:, ., (). Google Scholar |
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.
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.
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. Google Scholar |
[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.
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.
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.
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.
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.
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.
doi: 10.1016/0167-2789(94)90043-4. |
[10] |
M. W. Hirsch, Convergent activation dynamics in continuous time networks,, Neural Netw., 2 (1989), 331.
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.
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.
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.
doi: 10.1109/81.269055. |
[14] |
D. G. Kelly, Stability in contractive nonlinear neural networks,, IEEE Trans. Biomed. Eng., 3 (1990), 231.
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.
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. Google Scholar |
[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.
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.
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.
|
[20] |
Z. Orman, New sufficient conditions for global stability of neutral-type neural networks with time delays,, Neurocomputing, 97 (2012), 141.
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.
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.
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.
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.
doi: 10.1016/j.neucom.2005.03.003. |
[25] |
W. Walter, Analysis I,, second ed., (1990). Google Scholar |
[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. Google Scholar |
[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.
doi: 10.1162/08997660152469350. |
[28] |
J. Wu, Symmetric functional-differential equations and neural networks with memory,, Trans. Am. Math. Soc., 350 (1999), 4799.
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.
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.
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.
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).
doi: 10.1007/b105056. |
[33] |
W. Zhang, A weak condition of globally asymptotic stability for neural networks,, Applied Mathematics Letters, 19 (2006), 1210.
doi: 10.1016/j.aml.2006.01.009. |
[34] |
Available from:, ., (). Google Scholar |
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