Patterns of synchrony in lattice dynamical systems

Nonlinearity

Volumn 18, Issue 5, 2005, Pages 2193-2209

  Antoneli, Fernando ^a   Dias, Ana Paula S ^b   Golubitsky, Martin ^c   Wang, Yunjiao ^c  

^a UNIVERSITY OF SÃO PAULO   (Brazil)

^b UNIVERSITY OF PORTO   (Portugal)

^c University of Houston   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 23444460700     PISSN: 09517715     EISSN: None     Source Type: Journal    
DOI: 10.1088/0951-7715/18/5/016     Document Type: Article

References (25)

1. Antoneli F, Dias A P S, Golubitsky M and Wang Y Flow invariant subspaces for lattice dynamical systems Workshop on Bifurcation Theory and Spatio-Temporal Pattern Formation in PDE ed W Nagata and N S Namachchivaya Fields Institute Communications submitted
2. Armstrong M A 1988 Groups and Symmetry (Undergraduate Texts in Mathematics) (New York: Springer)
3. Brendel M and Roska T 2002 Adaptive image sensing and enhancement using the cellular neural network universal machine Int. J. Circuit Theory Appl. 30 287-312
4. Cahn J W 1960 Theory of crystal growth and interface motion in crystalline materials Acta Metall. 8 554-62
5. Cruz J M and Chua L O 1992 Design of high speed high density CNN's in CMOS technology Int. J. Circuit Theory Appl. 20 555-72
6. Chow S N 2003 Lattice dynamical systems Dynamical Systems (Lecture Notes in Mathematics vol 1822) ed S-N Chow et al (New York: Springer) pp 1-102
7. Chow S-N and Mallet-Paret J 1995 Pattern formation and spatial chaos in lattice dynamical systems: I IEEE Trans. Circuits Syst. 42 746-51
8. Chow S-N, Mallet-Paret J and Van Vleck E S 1996 Dynamics of lattice differential equations Int. J. Bifurcation Chaos Appl. Sci. Eng. 6 1605-21
9. Chow S-N, Mallet-Paret J and Van Vleck E S 1996 Pattern formation and spatial chaos in spatially discrete evolution equations Random Comput. Dyn. 4 109-78
10. Chua L O and Roska T 1993 The CNN paradigm IEEE Trans. Circuits Syst. 40 147-56
11. Chua L O and Yang L 1988 Cellular neural networks: theory IEEE Trans. Circuits Syst. 35 1257-72
12. Chua L O and Yang L 1988 Cellular neural networks: applications IEEE Trans. Circuits Syst. 35 1273-90
13. Cook H E, de Fontaine D and Hilliard J E 1969 A model for diffusion on cubic lattices and its applications to the early stages of ordering Acta Metall. 17 765-73
14. Epstein I R and Golubitsky M 1993 Symmetric patterns in linear arrays of coupled cells Chaos 3 1-5
15. Field M 2004 Combinatorial dynamics Dyn. Syst. 19 217-43
16. Gillis D and Golubitsky M 1997 Patterns in square arrays of coupled cells JMAA 208 487-509
17. Golubitsky M, Nicol M and Stewart I 2004 Some curious phenomena in coupled cell systems J. Nonlinear Sci. 14 119-236
18. Golubitsky M and Stewart I 2002 The Symmetry Perspective (Progress in Mathematics 200) (Basel: Birkhäuser)
19. Golubitsky M, Stewart I and Török A 2005 Patterns of synchrony in coupled cell networks with multiple arrows SIAM J. Appl. Dynam. Syst. 4 78-100
20. Hillert M 1961 A solid-solution model for inhomogeneous systems Acta Metall. 9 525-35
21. Mallet-Paret J 1996 Spatial patterns, spatial chaos and travelling waves in lattice differential equations Stochastic and Spatial Structures of Dynamical Systems ed S J Van Strien and S M Verdyun Lunel (Amsterdam: North-Holland) pp 105-29
22. Mallet-Paret J and Chow S-N 1995 Pattern formation and spatial chaos in lattice dynamical systems: II IEEE Trans. Circuits Syst. 42 752-56
23. Stewart I, Golubitsky M and Pivato M 2003 Symmetry groupoids and patterns of synchrony in coupled cell networks SIAM J. Appl. Dyn. Syst. 2 609-46
24. Thiran P, Crounse K R, Chua L O and Hasler M 1995 Pattern formation properties of autonomous cellular neural networks IEEE Trans. Circuits Syst. 42 757-74
25. Wang Y and Golubitsky M 2005 Two-color patterns of synchrony in lattice dynamical systems Nonlinearity 18 631-57