-
1
-
-
0028468031
-
How delays affect neural dynamics and learning
-
Baldi P., Atiya F. How delays affect neural dynamics and learning. IEEE Trans. Neural Netw. 1994, 4:612-621.
-
(1994)
IEEE Trans. Neural Netw.
, vol.4
, pp. 612-621
-
-
Baldi, P.1
Atiya, F.2
-
2
-
-
0003095221
-
The solution of equations by iteration
-
Coppel W.A. The solution of equations by iteration. Proc. Cambridge Philos. Soc. 1955, 51:41-43.
-
(1955)
Proc. Cambridge Philos. Soc.
, vol.51
, pp. 41-43
-
-
Coppel, W.A.1
-
3
-
-
0023932252
-
Stability of discrete one-dimensional population models
-
Cull P. Stability of discrete one-dimensional population models. Bull. Math. Biol. 1988, 50:67-75.
-
(1988)
Bull. Math. Biol.
, vol.50
, pp. 67-75
-
-
Cull, P.1
-
4
-
-
40849097852
-
Global attractors for difference equations dominated by one-dimensional maps
-
El-Morshedy H.A., Jiménez López V. Global attractors for difference equations dominated by one-dimensional maps. J. Difference Equ. Appl. 2008, 14:391-410.
-
(2008)
J. Difference Equ. Appl.
, vol.14
, pp. 391-410
-
-
El-Morshedy, H.A.1
Jiménez López, V.2
-
5
-
-
0003504382
-
An Introduction to Difference Equation
-
Springer, New York
-
Elaydi S. An Introduction to Difference Equation. Undergrad. Texts Math. 2005, Springer, New York. third ed.
-
(2005)
Undergrad. Texts Math.
-
-
Elaydi, S.1
-
6
-
-
0034693565
-
On a planar system modelling a neuron network with memory
-
Faria T. On a planar system modelling a neuron network with memory. J. Differential Equations 2000, 168:129-149.
-
(2000)
J. Differential Equations
, vol.168
, pp. 129-149
-
-
Faria, T.1
-
7
-
-
0000840164
-
Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation
-
Faria T., Magalhaes L.T. Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation. J. Differential Equations 1995, 122:181-200.
-
(1995)
J. Differential Equations
, vol.122
, pp. 181-200
-
-
Faria, T.1
Magalhaes, L.T.2
-
9
-
-
0001075269
-
Stability in asymmetric Hopfield nets with transmission delays
-
Gopalsamy G.K., He X.Z. Stability in asymmetric Hopfield nets with transmission delays. Phys. D 1994, 76:344-358.
-
(1994)
Phys. D
, vol.76
, pp. 344-358
-
-
Gopalsamy, G.K.1
He, X.Z.2
-
10
-
-
36849021007
-
Two-parameter bifurcations in a network of two neurons with multiple delays
-
Guo S., Chen Y., Wu J. Two-parameter bifurcations in a network of two neurons with multiple delays. J. Differential Equations 2008, 244:444-486.
-
(2008)
J. Differential Equations
, vol.244
, pp. 444-486
-
-
Guo, S.1
Chen, Y.2
Wu, J.3
-
12
-
-
0020118274
-
Neural networks and physical systems with emergent collective computational abilities
-
Hopfield J. Neural networks and physical systems with emergent collective computational abilities. Proc. Natl. Acad. Sci. USA 1982, 79:2554-2558.
-
(1982)
Proc. Natl. Acad. Sci. USA
, vol.79
, pp. 2554-2558
-
-
Hopfield, J.1
-
13
-
-
0004469897
-
Neurons with graded response have collective computational properties like those of two-state neurons
-
Hopfield J. Neurons with graded response have collective computational properties like those of two-state neurons. Proc. Natl. Acad. Sci. USA 1984, 81:3088-3092.
-
(1984)
Proc. Natl. Acad. Sci. USA
, vol.81
, pp. 3088-3092
-
-
Hopfield, J.1
-
14
-
-
0038381865
-
Nonlinear waves in networks of neurons with delayed feedback: Pattern formation and continuation
-
Huang L., Wu J. Nonlinear waves in networks of neurons with delayed feedback: Pattern formation and continuation. SIAM J. Math. Anal. 2003, 34:836-860.
-
(2003)
SIAM J. Math. Anal.
, vol.34
, pp. 836-860
-
-
Huang, L.1
Wu, J.2
-
15
-
-
36249025544
-
Global stability of a class of scalar nonlinear delay differential equations
-
Ivanov A.F., Liz E., Trofimchuk S. Global stability of a class of scalar nonlinear delay differential equations. Differ. Equ. Dyn. Syst. 2003, 11:33-54.
-
(2003)
Differ. Equ. Dyn. Syst.
, vol.11
, pp. 33-54
-
-
Ivanov, A.F.1
Liz, E.2
Trofimchuk, S.3
-
18
-
-
33847750617
-
Local stability implies global stability in some one-dimensional discrete single-species models
-
Liz E. Local stability implies global stability in some one-dimensional discrete single-species models. Discrete Contin. Dyn. Syst. Ser. B 2007, 7:191-199.
-
(2007)
Discrete Contin. Dyn. Syst. Ser. B
, vol.7
, pp. 191-199
-
-
Liz, E.1
-
19
-
-
17744386691
-
Attractivity properties of infinite delay Mackey-Glass type equations
-
Liz E., Martínez C., Trofimchuk S. Attractivity properties of infinite delay Mackey-Glass type equations. Differential Integral Equations 2002, 15:875-896.
-
(2002)
Differential Integral Equations
, vol.15
, pp. 875-896
-
-
Liz, E.1
Martínez, C.2
Trofimchuk, S.3
-
20
-
-
17744367652
-
A global stability criterion for a family of delayed population models
-
Liz E., Pinto M., Tkachenko V., Trofimchuk S. A global stability criterion for a family of delayed population models. Quart. Appl. Math. 2005, 63:56-70.
-
(2005)
Quart. Appl. Math.
, vol.63
, pp. 56-70
-
-
Liz, E.1
Pinto, M.2
Tkachenko, V.3
Trofimchuk, S.4
-
21
-
-
69549111437
-
On the global attractor of delay differential equations with unimodal feedback
-
Liz E., Röst G. On the global attractor of delay differential equations with unimodal feedback. Discrete Contin. Dyn. Syst. 2009, 24:1215-1224.
-
(2009)
Discrete Contin. Dyn. Syst.
, vol.24
, pp. 1215-1224
-
-
Liz, E.1
Röst, G.2
-
22
-
-
2442502476
-
A global stability criterion for scalar functional differential equations
-
Liz E., Tkachenko V., Trofimchuk S. A global stability criterion for scalar functional differential equations. SIAM J. Math. Anal. 2003, 35:596-622.
-
(2003)
SIAM J. Math. Anal.
, vol.35
, pp. 596-622
-
-
Liz, E.1
Tkachenko, V.2
Trofimchuk, S.3
-
23
-
-
67650714417
-
Multistability and gluing bifurcation to butterflies in coupled networks with non-monotonic feedback
-
Ma J., Wu J. Multistability and gluing bifurcation to butterflies in coupled networks with non-monotonic feedback. Nonlinearity 2009, 22:1383-1412.
-
(2009)
Nonlinearity
, vol.22
, pp. 1383-1412
-
-
Ma, J.1
Wu, J.2
-
24
-
-
0001842517
-
Global continuation and asymptotic behaviour for periodic solutions of a differential-delay equation
-
Mallet-Paret J., Nussbaum R. Global continuation and asymptotic behaviour for periodic solutions of a differential-delay equation. Ann. Mat. Pura Appl. 1986, 145:33-128.
-
(1986)
Ann. Mat. Pura Appl.
, vol.145
, pp. 33-128
-
-
Mallet-Paret, J.1
Nussbaum, R.2
-
25
-
-
0000145206
-
A differential-delay equation arising in optics and physiology
-
Mallet-Paret J., Nussbaum R. A differential-delay equation arising in optics and physiology. SIAM J. Math. Anal. 1989, 20:249-292.
-
(1989)
SIAM J. Math. Anal.
, vol.20
, pp. 249-292
-
-
Mallet-Paret, J.1
Nussbaum, R.2
-
26
-
-
0000256610
-
Stability of analog neural networks with delay
-
Marcus C.M., Westervelt R.M. Stability of analog neural networks with delay. Phys. Rev. A 1989, 39:347-359.
-
(1989)
Phys. Rev. A
, vol.39
, pp. 347-359
-
-
Marcus, C.M.1
Westervelt, R.M.2
-
27
-
-
0027148066
-
Associative memory with non-monotone dynamics
-
Morita M. Associative memory with non-monotone dynamics. Neural Netw. 1993, 6:115-123.
-
(1993)
Neural Netw.
, vol.6
, pp. 115-123
-
-
Morita, M.1
-
28
-
-
34548678972
-
Attractor minimal sets for non-autonomous delay functional differential equations with applications for neural networks
-
Novo S., Obaya R., Sanz A. Attractor minimal sets for non-autonomous delay functional differential equations with applications for neural networks. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 2005, 461:2767-2783.
-
(2005)
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.
, vol.461
, pp. 2767-2783
-
-
Novo, S.1
Obaya, R.2
Sanz, A.3
-
29
-
-
33750634090
-
n symmetric delay differential systems
-
n symmetric delay differential systems. J. Differential Equations 2007, 232:521-543.
-
(2007)
J. Differential Equations
, vol.232
, pp. 521-543
-
-
Peng, M.1
-
30
-
-
36348976487
-
Domain decomposition method for the global dynamics of delay differential equations with unimodal feedback
-
Röst G., Wu J. Domain decomposition method for the global dynamics of delay differential equations with unimodal feedback. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 2007, 463:2655-2669.
-
(2007)
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.
, vol.463
, pp. 2655-2669
-
-
Röst, G.1
Wu, J.2
-
31
-
-
34248517099
-
Delay differential equations in single species dynamics
-
Springer, Dordrecht, Delay Differential Equations and Applications
-
Ruan S. Delay differential equations in single species dynamics. NATO Sci. Ser. II Math. Phys. Chem. 2006, vol. 205:477-517. Springer, Dordrecht.
-
(2006)
NATO Sci. Ser. II Math. Phys. Chem.
, vol.205
, pp. 477-517
-
-
Ruan, S.1
-
32
-
-
56349172264
-
Convergent dynamics for multistable delayed neural networks
-
Shih C.W., Tseng J.P. Convergent dynamics for multistable delayed neural networks. Nonlinearity 2008, 21:2361-2389.
-
(2008)
Nonlinearity
, vol.21
, pp. 2361-2389
-
-
Shih, C.W.1
Tseng, J.P.2
-
33
-
-
0003270907
-
Monotone Dynamical Systems. An Introduction to the Theory of Competitive and Cooperative Systems
-
AMS, Providence, RI
-
Smith H.L. Monotone Dynamical Systems. An Introduction to the Theory of Competitive and Cooperative Systems. Math. Surveys Monogr. 1995, vol. 41. AMS, Providence, RI.
-
(1995)
Math. Surveys Monogr.
, vol.41
-
-
Smith, H.L.1
-
34
-
-
22544452748
-
Global exponential stability and periodic solutions of Cohen-Grossberg neural networks with continuously distributed delays
-
Sun J., Wan L. Global exponential stability and periodic solutions of Cohen-Grossberg neural networks with continuously distributed delays. Phys. D 2005, 208:1-20.
-
(2005)
Phys. D
, vol.208
, pp. 1-20
-
-
Sun, J.1
Wan, L.2
-
35
-
-
70350650732
-
The existence and global exponential stability of a periodic solution of a class of delay differential equations
-
Tang X.-H., Zou X. The existence and global exponential stability of a periodic solution of a class of delay differential equations. Nonlinearity 2009, 22:2423-2442.
-
(2009)
Nonlinearity
, vol.22
, pp. 2423-2442
-
-
Tang, X.-H.1
Zou, X.2
-
37
-
-
0035276184
-
Stabilization role of inhibitory self-connections in a delayed neural network
-
van den Driessche P., Wu J., Zou X. Stabilization role of inhibitory self-connections in a delayed neural network. Phys. D 2001, 150:84-90.
-
(2001)
Phys. D
, vol.150
, pp. 84-90
-
-
van den Driessche, P.1
Wu, J.2
Zou, X.3
-
38
-
-
0032298907
-
Global attractivity in delayed Hopfield neural network models
-
van den Driessche P., Zou X. Global attractivity in delayed Hopfield neural network models. SIAM J. Appl. Math. 1998, 58:1878-1890.
-
(1998)
SIAM J. Appl. Math.
, vol.58
, pp. 1878-1890
-
-
van den Driessche, P.1
Zou, X.2
-
39
-
-
6444228136
-
Global existence of periodic solutions in a tri-neuron network model with delays
-
Wei J., Li M. Global existence of periodic solutions in a tri-neuron network model with delays. Phys. D 2004, 198:106-119.
-
(2004)
Phys. D
, vol.198
, pp. 106-119
-
-
Wei, J.1
Li, M.2
-
40
-
-
33646864830
-
Symmetric functional differential equations and neural networks with memory
-
Wu J. Symmetric functional differential equations and neural networks with memory. Trans. Amer. Math. Soc. 1998, 350:4799-4838.
-
(1998)
Trans. Amer. Math. Soc.
, vol.350
, pp. 4799-4838
-
-
Wu, J.1
-
41
-
-
10944272216
-
Introduction to Neural Dynamics and Signal Transmission Delay
-
Walter de Gruyter & Co., Berlin
-
Wu J. Introduction to Neural Dynamics and Signal Transmission Delay. de Gruyter Ser. Nonlinear Anal. Appl. 2001, vol. 6. Walter de Gruyter & Co., Berlin.
-
(2001)
de Gruyter Ser. Nonlinear Anal. Appl.
, vol.6
-
-
Wu, J.1
-
42
-
-
77958091083
-
Maps dynamics versus dynamics of associated delay reaction-diffusion equation with a Neumann condition
-
Yi T., Zou X. Maps dynamics versus dynamics of associated delay reaction-diffusion equation with a Neumann condition. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 2010, 466:2955-2973.
-
(2010)
Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci.
, vol.466
, pp. 2955-2973
-
-
Yi, T.1
Zou, X.2
-
43
-
-
79961208216
-
Global dynamics of a delay differential equation with spatial non-locality in an unbounded domain
-
Yi T., Zou X. Global dynamics of a delay differential equation with spatial non-locality in an unbounded domain. J. Differential Equations 2011, 251:2598-2611.
-
(2011)
J. Differential Equations
, vol.251
, pp. 2598-2611
-
-
Yi, T.1
Zou, X.2
-
44
-
-
0027224451
-
Capacity of associative memory using a nonmonotonic neuron model
-
Yoshizawa S., Morita M., Amari S. Capacity of associative memory using a nonmonotonic neuron model. Neural Netw. 1993, 6:167-176.
-
(1993)
Neural Netw.
, vol.6
, pp. 167-176
-
-
Yoshizawa, S.1
Morita, M.2
Amari, S.3
-
45
-
-
83055181325
-
Global stability for non-monotone delay equations (with application to a model of blood cell production)
-
Yuan Y., Zhao X.Q. Global stability for non-monotone delay equations (with application to a model of blood cell production). J. Differential Equations 2012, 252:2189-2209.
-
(2012)
J. Differential Equations
, vol.252
, pp. 2189-2209
-
-
Yuan, Y.1
Zhao, X.Q.2
-
46
-
-
58049177388
-
Necessary and sufficient conditions for global attractivity of Hopfield-type neural networks with time delays
-
Zhang S., Ma W., Kuang Y. Necessary and sufficient conditions for global attractivity of Hopfield-type neural networks with time delays. Rocky Mountain J. Math. 2008, 38:1829-1840.
-
(2008)
Rocky Mountain J. Math.
, vol.38
, pp. 1829-1840
-
-
Zhang, S.1
Ma, W.2
Kuang, Y.3
|