Designing the dynamics of globally coupled oscillators

Progress of Theoretical Physics

Volumn 122, Issue 3, 2009, Pages 611-630

  Orosz, Gábor ^a,b   Moehlis, Jeff ^a   Ashwin, Peter ^b  

^a University of California   (United States)

^b UNIVERSITY OF EXETER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 73949108157     PISSN: 0033068X     EISSN: 13474081     Source Type: Journal    
DOI: 10.1143/PTP.122.611     Document Type: Article

References (38)

1. D. G. Aronson, M. Krupa and P. Ashwin, J. of Nonlinear Science 6 (1996), 85.
2. P. Ashwin and J. Borresen, Phys. Rev. E 70 (2004), 026203.
3. P. Ashwin and J. Borresen, Phys. Lett. A 347 (2005), 208.
4. P. Ashwin, G. Orosz, J. Wordsworth and S. Townley, SIAM J. on Applied Dynamical Systems 6 (2007), 728.
5. P. Ashwin and J. W. Swift, J. of Nonlinear Science 2 (1992), 69.
6. E. Brown, P. Holmes and J. Moehlis, in Perspectives and Problems in Nonlinear Science: A Celebratory Volume in Honor of Larry Sirovich, ed. E. Kaplan, J. E. Marsden and K. R. Sreenivasan (Springer, 2003), p. 183.
7. E. Brown, J. Moehlis and P. Holmes, Neural Computation 16 (2004), 673.
8. S. A. Campbell, in Handbook of Brain Connectivity, ed. V. K. Jirsa and A. R. McIntosh (Springer, 2007), p. 65.
9. H. Daido, Physica D 91 (1996), 24.
10. B. Ermentrout and T.-W. Ko, Philos. Trans. R. Soc. A 367 (2009), 1097.
11. G. B. Ermentrout, SIAM J. on Applied Mathematics 52 (1992), 1665.
12. C. M. Gonzales, C. Masoller, M. C. Torrent and J. Garcia-Ojalvo, Europhys. Lett. 79 (2007), 64003.
13. F. C. Hoppensteadt and E. M. Izhikevich, Weakly Connected Neural Networks, Applied Mathematical Sciences Vol. 126 (Springer, 1997).
14. F. C. Hoppensteadt and E. M. Izhikevich, Phys. Rev. Lett. 82 (1999), 2983.
15. F. C. Hoppensteadt and E. M. Izhikevich, IEEE Trans. on Neural Networks 11 (2000), 734.
16. E. M. Izhikevich, Phys. Rev. E 58 (1998), 905.
17. M. Kimura and J. Moehlis, SIAM J. on Applied Dynamical Systems 7 (2008), 1191.
18. I. Z. Kiss, C. G. Rusin, H. Kori and J. L. Hudson, Science 316 (2007), 1886.
19. Y. Kobayashi and H. Kori, New J. Phys. 11 (2009), 033018.
20. H. Kori, Phys. Rev. E 68 (2003), 021919.
21. H. Kori and Y. Kuramoto, Phys. Rev. E 63 (2001), 046214.
22. H. Kori, C. G. Rusin, I. Z. Kiss and J. L. Hudson, Chaos 18 (2008), 026111.
23. Y. Kuramoto, Lecture Notes in Phys. 39, ed. H. Araki (Springer, 1975), p. 420.
24. C. Mead and L. Conway, Introduction to VLSI Systems (Addison-Wesley, 1980).
25. R. M. Memmesheimer and M. Timme, Physica D 224 (2006), 182.
26. R. M. Memmesheimer and M. Timme, Phys. Rev. Lett. 97 (2006), 188101.
27. I. Mezić, Lecture Notes on Methods of Operator Theory in Dynamical Systems, Preprint, University of California, Santa Barbara, 2009.
28. J. von Neumann, The Computer and the Brain (Yale University Press, 1958).
29. K. Okuda, Physica D 63 (1993), 424.
30. R. Olfati-Saber and R. M. Murray, IEEE Trans. on Automatic Control 49 (2004), 1520.
31. G. Orosz, P. Ashwin and S. Townley, IEEE Trans. on Neural Networks 20 (2009), 1135.
32. D. A. Paley, N. E. Leonard, R. Sepulchre, D. Grunbaum and J. K. Parrish, IEEE Control Systems Magazine 27 (2007), 89.
33. M. I. Rabinovich, R. Huerta, P. Varona and V. S. Afraimovich, Biological Cybernetics 95 (2006), 519.
34. M. I. Rabinovich, P. Varona, A. I. Selverston and H. D. I. Abarbanel, Rev. Mod. Phys. 78 (2006), 1213.
35. T. Roska and L. O. Chua, IEEE Trans. on Circuits and Systems II - Analog and Digital Signal Processing 40 (1993), 163.
36. R. Sepulchre, D. Paley and N. E. Leonard, IEEE Trans. on Automatic Control 52 (2007), 811.
37. S. H. Strogatz, Physica D 143 (2000), 1.
38. R. S. Varga, Geršgorin and His Circles (Springer, 2004).