-
2
-
-
79955521712
-
-
A. Canada, P. Drabek, A. Fonda Eds. Amsterdam The Netherlands: Elsevier, [Online]. Available
-
M. Hirsch and H. Smith, Monotone dynamical systems in Handbook of Differential Equations, Ordinary Differential Equations (Second Volume), A. Canada, P. Drabek, A. Fonda, Eds. Amsterdam, The Netherlands: Elsevier, 2005 [Online]. Available: http://math.la.asu.edu/halsmith/book.html
-
(2005)
Monotone dynamical systems in Handbook of Differential Equations, Ordinary Differential Equations (Second Volume)
-
-
Hirsch, M.1
Smith, H.2
-
3
-
-
0000885375
-
Systems of differential equations which are competitive or cooperative. I: Limit sets
-
M. W. Hirsch, Systems of differential equations which are competitive or cooperative. I: Limit sets SIAM J. Math. Anal., 13, 167-179, 1982.
-
(1982)
SIAM J. Math. Anal.
, vol.13
, pp. 167-179
-
-
Hirsch, M.W.1
-
4
-
-
0001176145
-
Systems of differential equations which are competitive or cooperative. II: Convergence almost everywhere
-
M. W. Hirsch, Systems of differential equations which are competitive or cooperative. II: Convergence almost everywhere SIAM J. Math. Anal., 16, 423-439, 1985.
-
(1985)
SIAM J. Math. Anal.
, vol.16
, pp. 423-439
-
-
Hirsch, M.W.1
-
5
-
-
33745815315
-
Stability and convergence in strongly monotone dynamical systems
-
M. W. Hirsch, Stability and convergence in strongly monotone dynamical systems J. Reine Angew. Math., 383, 1-53, 1988.
-
(1988)
J. Reine Angew. Math.
, vol.383
, pp. 1-53
-
-
Hirsch, M.W.1
-
6
-
-
0000168647
-
Quasi convergence and stability for strongly order-preserving semiflows
-
H. L. Smith and H. R. Thieme, Quasi convergence and stability for strongly order-preserving semiflows SIAM J. Math. Anal., 21, 3, 673-692, 1990.
-
(1990)
SIAM J. Math. Anal.
, vol.21
, Issue.3
, pp. 673-692
-
-
Smith, H.L.1
Thieme, H.R.2
-
7
-
-
0001676484
-
Strongly order preserving semiflows generated by functional differential equations
-
May
-
H. L. Smith and H. Thieme, Strongly order preserving semiflows generated by functional differential equations J. Differential Equations, 93, 332-363, May 1991.
-
(1991)
J. Differential Equations
, vol.93
, pp. 332-363
-
-
Smith, H.L.1
Thieme, H.2
-
8
-
-
0001113507
-
Convergence for strongly order-preserving semiflows
-
H. L. Smith and H. R. Thieme, Convergence for strongly order-preserving semiflows SIAM J. Math. Anal., 22, 4, 1081-1101, 1991.
-
(1991)
SIAM J. Math. Anal.
, vol.22
, Issue.4
, pp. 1081-1101
-
-
Smith, H.L.1
Thieme, H.R.2
-
11
-
-
33646004257
-
A cooperative system which does not satisfy the limit set dichotomy
-
DOI 10.1016/j.jde.2005.07.026, PII S0022039605002810
-
E. D. Sontag and Y.Wang, A cooperative system which does not satisfy the limit set dichotomy J. Differential Equations, 224, 373-384, 2006. (Pubitemid 43592017)
-
(2006)
Journal of Differential Equations
, vol.224
, Issue.2
, pp. 373-384
-
-
Sontag, E.D.1
Wang, Y.2
-
12
-
-
0024909476
-
Convergent activation dynamics in continuous time networks
-
DOI 10.1016/0893-6080(89)90018-X
-
M. Hirsch, Convergent activation dynamics in continuous time networks Neural Netw., 2, 331-349, 1989. (Pubitemid 20609006)
-
(1989)
Neural Networks
, vol.2
, Issue.5
, pp. 331-349
-
-
Hirsch Morris, W.1
-
13
-
-
0025632457
-
Stability of a class of nonreciprocal neural networks
-
Dec.
-
L. O. Chua and T. Roska, Stability of a class of nonreciprocal neural networks IEEE Trans. Circuits Syst., 37, 1520-1527, Dec. 1990.
-
(1990)
IEEE Trans. Circuits Syst.
, vol.37
, pp. 1520-1527
-
-
Chua, L.O.1
Roska, T.2
-
14
-
-
0026882236
-
Stability and dynamics of delay-type general and cellular neural networks
-
Jun.
-
T. Roska, C. W.Wu,M. Balsi, L. O. Chua, Stability and dynamics of delay-type general and cellular neural networks IEEE Trans. Circuits Syst. I, 39, 487-490, Jun. 1992.
-
(1992)
IEEE Trans. Circuits Syst. I
, vol.39
, pp. 487-490
-
-
Roska, T.1
Wu, C.W.2
Balsi, M.3
Chua, L.O.4
-
16
-
-
0024088955
-
Cellular neural networks: Theory
-
Oct.
-
L. O. Chua and L. Yang, Cellular neural networks: Theory IEEE Trans. Circuits Syst., 35, 10, 1257-1272, Oct. 1988.
-
(1988)
IEEE Trans. Circuits Syst.
, vol.35
, Issue.10
, pp. 1257-1272
-
-
Chua, L.O.1
Yang, L.2
-
17
-
-
0024765401
-
Analysis and synthesis of a class of neural networks: Linear systems operating on a closed hypercube
-
DOI 10.1109/31.41297
-
J. Li, A. N. Michel, W. Porod, Analysis and synthesis of a class of neural networks: Linear systems operating on a closed hypercube IEEE Trans. Circuits Syst., 36, 1405-1422, Nov. 1989. (Pubitemid 20642393)
-
(1989)
IEEE transactions on circuits and systems
, vol.36
, Issue.11
, pp. 1405-1422
-
-
Li Jian-Hua1
Michel Anthony, N.2
Porod Wolfgang3
-
18
-
-
0024016062
-
Neural networks for nonlinear programming
-
May
-
M. P. Kennedy and L. O. Chua, Neural networks for nonlinear programming IEEE Trans. Circuits Syst. I, 35, 554-562, May 1988.
-
(1988)
IEEE Trans. Circuits Syst. I
, vol.35
, pp. 554-562
-
-
Kennedy, M.P.1
Chua, L.O.2
-
19
-
-
0032179258
-
Pyramidal cells: A novel class of adaptive coupling cells and their applications for cellular neural networks
-
PII S1057712298074224
-
R. Dogaru, K. R. Crounse, L. O. Chua, Pyramidal cells: A novel class of adaptive coupling cells and their applications for cellular neural networks IEEE Trans. Circuits Syst. I, 45, 1077-1090, Oct. 1998. (Pubitemid 128745935)
-
(1998)
IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
, vol.45
, Issue.10
, pp. 1077-1090
-
-
Dogaru, R.1
Crounse, K.R.2
Chua, L.O.3
-
20
-
-
0027595876
-
A multilevel neural network for A/D conversion
-
May
-
J. D. Yu and R. W. Newcomb, A multilevel neural network for A/D conversion IEEE Trans. Neural Netw., 4, 470-483, May 1993.
-
(1993)
IEEE Trans. Neural Netw.
, vol.4
, pp. 470-483
-
-
Yu, J.D.1
Newcomb, R.W.2
-
22
-
-
0034747507
-
Complete stability for a class of cellular neural networks
-
C. W. Shih, Complete stability for a class of cellular neural networks Int. J. Bifurcation Chaos, 11, 169-177, 2001.
-
(2001)
Int. J. Bifurcation Chaos
, vol.11
, pp. 169-177
-
-
Shih, C.W.1
-
23
-
-
79955524731
-
-
presented at the CNNA2010, Berkeley, CA, Feb. 3-5
-
M. Di Marco, M. Forti, M. Grazzini, L. Pancioni, The dichotomy of omega-limit sets fails for cooperative standard CNNs presented at the CNNA2010, Berkeley, CA, Feb. 3-5, 2010.
-
(2010)
The Dichotomy of Omega-Limit Sets Fails for Cooperative Standard CNNs
-
-
Di Marco, M.1
Forti, M.2
Grazzini, M.3
Pancioni, L.4
-
24
-
-
0020118274
-
Neural networks and physical systems with emergent collective computational abilities
-
Apr.
-
J. Hopfield, Neural networks and physical systems with emergent collective computational abilities Proc. Nat. Acad. Sci., 79, 2554-2558, Apr. 1982.
-
(1982)
Proc. Nat. Acad. Sci.
, vol.79
, pp. 2554-2558
-
-
Hopfield, J.1
-
25
-
-
0024054127
-
Qualitative analysis and synthesis of a class of neural networks
-
Aug.
-
J. H. Li, A. N. Michel, W. Porod, Qualitative analysis and synthesis of a class of neural networks IEEE Trans. Circuits Syst., 35, 8, 976-986, Aug. 1988.
-
(1988)
IEEE Trans. Circuits Syst.
, vol.35
, Issue.8
, pp. 976-986
-
-
Li, J.H.1
Michel, A.N.2
Porod, W.3
-
26
-
-
0024610496
-
Qualitative analysis of neural networks
-
Feb.
-
A. N. Michel, J. A. Farrell, W. Porod, Qualitative analysis of neural networks IEEE Trans. Circuits Syst., 36, 2, 229-243, Feb. 1989.
-
(1989)
IEEE Trans. Circuits Syst.
, vol.36
, Issue.2
, pp. 229-243
-
-
Michel, A.N.1
Farrell, J.A.2
Porod, W.3
-
27
-
-
0027569219
-
On stability of cellular neural networks with delay
-
P. P. Civalleri, M. Gilli, L. Pandolfi, On stability of cellular neural networks with delay IEEE Trans. Circuits Syst. I, 40, 157-165, 1993.
-
(1993)
IEEE Trans. Circuits Syst. I
, vol.40
, pp. 157-165
-
-
Civalleri, P.P.1
Gilli, M.2
Pandolfi, L.3
-
28
-
-
10944255986
-
Absolute stability of analytic neural networks: An approach based on finite trajectory length
-
DOI 10.1109/TCSI.2004.838143
-
M. Forti and A. Tesi, Absolute stability of analytic neural networks: An approach based on finite trajectory length IEEE Trans. Circuits Syst. I, 51, 12, 2460-2469, Dec. 2004. (Pubitemid 40009467)
-
(2004)
IEEE Transactions on Circuits and Systems I: Regular Papers
, vol.51
, Issue.12
, pp. 2460-2469
-
-
Forti, M.1
Tesi, A.2
-
29
-
-
58049206270
-
Lyapunov method and convergence of the full-range model of CNNs
-
Dec.
-
M. Di Marco, M. Forti, M. Grazzini, P. Nistri, L. Pancioni, Lyapunov method and convergence of the full-range model of CNNs IEEE Trans. Circuits Syst. I, 55, 11, 3528-3541, Dec. 2008.
-
(2008)
IEEE Trans. Circuits Syst. I
, vol.55
, Issue.11
, pp. 3528-3541
-
-
Di Marco, M.1
Forti, M.2
Grazzini, M.3
Nistri, P.4
Pancioni, L.5
-
30
-
-
0029358102
-
Minimum-seeking properties of analog neural networks with multilinear objective functions
-
Aug.
-
M. Vidyasagar, Minimum-seeking properties of analog neural networks with multilinear objective functions IEEE Trans. Autom. Control, 40, 1359-1375, Aug. 1995.
-
(1995)
IEEE Trans. Autom. Control
, vol.40
, pp. 1359-1375
-
-
Vidyasagar, M.1
-
31
-
-
0037274395
-
Absolute exponential stability of a class of continuous- time recurrent neural networks
-
Jan.
-
S. Hu and J.Wang, Absolute exponential stability of a class of continuous- time recurrent neural networks IEEE Trans. Neural Netw., 14, 1, 35-45, Jan. 2003.
-
(2003)
IEEE Trans. Neural Netw.
, vol.14
, Issue.1
, pp. 35-45
-
-
Hu, S.1
Wang, J.2
-
32
-
-
33645831985
-
Complete stability of cellular neural networks with time-varying delays
-
Apr.
-
Z. Zeng and J. Wang, Complete stability of cellular neural networks with time-varying delays IEEE Trans. Circuits Syst. I, 53, 4, 944-955, Apr. 2006.
-
(2006)
IEEE Trans. Circuits Syst. I
, vol.53
, Issue.4
, pp. 944-955
-
-
Zeng, Z.1
Wang, J.2
-
33
-
-
58049205433
-
Convergence analysis of a class of nonsmooth gradient systems
-
Dec.
-
W. Lu and J. Wang, Convergence analysis of a class of nonsmooth gradient systems IEEE Trans. Circuits Syst. I, 55, 11, 3514-3527, Dec. 2008.
-
(2008)
IEEE Trans. Circuits Syst. I
, vol.55
, Issue.11
, pp. 3514-3527
-
-
Lu, W.1
Wang, J.2
-
34
-
-
0036647798
-
Existence and characterization of limit cycles in nearly symmetric neural networks
-
DOI 10.1109/TCSI.2002.800481, PII 1011092002800481
-
M. Di Marco, M. Forti, A. Tesi, Existence and characterization of limit cycles in nearly symmetric neural networks IEEE Trans. Circuits Syst. I, 49, 7, 979-992, Jul. 2002. (Pubitemid 34861844)
-
(2002)
IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
, vol.49
, Issue.7
, pp. 979-992
-
-
Di Marco, M.1
Forti, M.2
Tesi, A.3
-
35
-
-
85042022325
-
Limit set dichotomy and convergence of semiflows defined by cooperative standard CNNs
-
to be published
-
M. Di Marco, M. Forti, M. Grazzini, L. Pancioni, Limit set dichotomy and convergence of semiflows defined by cooperative standard CNNs Int. J. Bifurcation Chaos, to be published.
-
Int. J. Bifurcation Chaos
-
-
Di Marco, M.1
Forti, M.2
Grazzini, M.3
Pancioni, L.4
-
36
-
-
33646528724
-
-
Sceaux France: Editions Jacques Gabay
-
C. Kuratowski, Topologie I et II. Sceaux, France: Editions Jacques Gabay, 1992.
-
(1992)
Topologie I et II
-
-
Kuratowski, C.1
-
37
-
-
0001166664
-
Existence of nontrivial unstable sets for equilibriums of strongly order preserving systems
-
H. Matano, Existence of nontrivial unstable sets for equilibriums of strongly order preserving systems J. Fac. Sci. Univ. Tokio, 30, 645-673, 1984.
-
(1984)
J. Fac. Sci. Univ. Tokio
, vol.30
, pp. 645-673
-
-
Matano, H.1
-
38
-
-
30344457607
-
Convergence and stability for essentially strongly order-preserving semiflows
-
DOI 10.1016/j.jde.2005.04.002, PII S0022039605001786
-
T. Yi and L. Huang, Convergence and stability for essentially strongly order-preserving semiflows J. Differential Equations, 221, 1, 36-57, 2006. (Pubitemid 43056749)
-
(2006)
Journal of Differential Equations
, vol.221
, Issue.1
, pp. 36-57
-
-
Yi, T.1
Huang, L.2
-
39
-
-
34848895159
-
Dynamics of smooth essentially strongly orderpreserving semiflows with application to delay differential equations
-
T. Yi and L. Huang, Dynamics of smooth essentially strongly orderpreserving semiflows with application to delay differential equations J. Math. Anal. Appl., 338, 2, 1329-1339, 2008.
-
(2008)
J. Math. Anal. Appl.
, vol.338
, Issue.2
, pp. 1329-1339
-
-
Yi, T.1
Huang, L.2
-
40
-
-
1642581775
-
On the ω-limit set Dichotomy of Cooperating Kolmogorov Systems
-
DOI 10.1023/A:1026287609893
-
J. Jiang and Y. Wang, On the w-limit set dichotomy of cooperating kolmogorov systems Positivity, 7, 3, 185-194, 2003. (Pubitemid 38118199)
-
(2003)
Positivity
, vol.7
, Issue.3
, pp. 185-194
-
-
Jiang, J.1
Wang, Y.2
-
41
-
-
61849090861
-
Attractors in coherent systems of differential equations
-
D. Angeli, M. W. Hirsch, E. D. Sontag, Attractors in coherent systems of differential equations J. Differential Equations, 246, 3058-3076, 2009.
-
(2009)
J. Differential Equations
, vol.246
, pp. 3058-3076
-
-
Angeli, D.1
Hirsch, M.W.2
Sontag, E.D.3
|