Response of traveling waves to transient inputs in neural fields

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 85, Issue 2, 2012, Pages

  Kilpatrick, Zachary P ^a   Ermentrout, Bard ^a  

^a UNIVERSITY OF PITTSBURGH   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ADJOINTS; GLOBAL BIFURCATIONS; LIMIT-CYCLE OSCILLATORS; NEURAL FIELDS; NEURONAL NETWORKS; PHASE RESPONSE CURVES; SYNAPTIC CONNECTIONS; TIME-DEPENDENT; TRANSIENT STIMULATION; TRAVELING FRONT; TRAVELING PULSE; TRAVELING WAVE; WAVE RESPONSE;

CONVOLUTION; INTEGRODIFFERENTIAL EQUATIONS;

NEURAL NETWORKS;

EID: 84857544734     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.85.021910     Document Type: Article

References (60)

1. X.-J. Wang, Physiol. Rev. PHREA7 0031-9333 10.1152/physrev.00035.2008 90, 1195 (2010).
2. J.-Y. Wu, Neuroscientist 1073-8584 10.1177/1073858408317066 14, 487 (2008).
3. K. R. Delaney, A. Gelperin, M. S. Fee, J. A. Flores, R. Gervais, D. W. Tank, and D. Kleinfeld, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.91.2.669 91, 669 (1994).
4. F. Han, N. Caporale, and Y. Dan, Neuron NERNET 0896-6273 10.1016/j.neuron.2008.08.026 60, 321 (2008).
5. W. Xu, X. Huang, K. Takagaki, and J.-Y. Wu, Neuron NERNET 0896-6273 10.1016/j.neuron.2007.06.016 55, 119 (2007). (Pubitemid 46990819)
6. G. B. Ermentrout and D. Kleinfeld, Neuron NERNET 0896-6273 10.1016/S0896-6273(01)00178-7 29, 33 (2001). (Pubitemid 32108720)
7. D. Rubino, K. A. Robbins, and N. G. Hatsopoulos, Nature Neurosci. NANEFN 1097-6256 10.1038/nn1802 9, 1549 (2006). (Pubitemid 44862664)
8. R. J. Morgan and I. Soltesz, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.0801372105 105, 6179 (2008). (Pubitemid 351758419)
9. R. D. Chervin, P. A. Pierce, and B. W. Connors, J. Neurophysiol. 60, 1695 (1988).
10. D. J. Pinto, S. L. Patrick, W. C. Huang, and B. W. Connors, J. Neurosci. JNRSDS 0270-6474 10.1523/JNEUROSCI.2278-05.2005 25, 8131 (2005). (Pubitemid 41292108)
11. K. A. Richardson, S. J. Schiff, and B. J. Gluckman, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.028103 94, 028103 (2005). (Pubitemid 40620189)
12. S. Coombes, Biol. Cybern. BICYAF 0340-1200 10.1007/s00422-005-0574-y 93, 91 (2005). (Pubitemid 41205590)
13. P. C. Bressloff, J. Phys. A: Math. Theor. 1751-8113 10.1088/1751-8113/45/ 3/033001 45, 033001 (2012).
14. H. R. Wilson and J. D. Cowan, Biol. Cybern. 13, 55 (1973).
15. S. Amari, Biol. Cybern. BICYAF 0340-1200 10.1007/BF00337259 27, 77 (1977).
16. G. B. Ermentrout and J. D. Cowan, Biol. Cybern. BICYAF 0340-1200 10.1007/BF00336965 34, 137 (1979). (Pubitemid 10246235)
17. P. C. Bressloff, J. D. Cowan, M. Golubitsky, P. J. Thomas, and M. C. Wiener, Philos. Trans. R. Soc. London, Ser. B PTRBAE 0962-8436 10.1098/rstb.2000.0769 356, 299 (2001). (Pubitemid 32305007)
18. G. B. Ermentrout and J. B. McLeod, Proc. R. Soc. Edinburgh, Sect. A PEAMDU 0308-2105 10.1017/S030821050002583X 123, 461 (1993).
19. M. Idiart and L. Abbott, Network NEWKEB 0954-898X 10.1088/0954-898X/4/3/ 003 4, 285 (1993).
20. P. C. Bressloff, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(01)00266-4 155, 83 (2001). (Pubitemid 32499019)
21. D. J. Pinto and G. B. Ermentrout, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/S0036139900346453 62, 206 (2001).
22. C. R. Laing, W. C. Troy, B. Gutkin, and G. B. Ermentrout, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/S0036139901389495 63, 62 (2002).
23. A. Hutt, M. Bestehorn, and T. Wennekers, Network NEWKEB 0954-898X 10.1088/0954-898X/14/2/310 14, 351 (2003). (Pubitemid 38002287)
24. A. Hutt and F. M. Atay, Chaos Solitons Fractals CSFOEH 0960-0779 10.1016/j.chaos.2005.10.091 32, 547 (2007). (Pubitemid 44537744)
25. R. Ben-Yishai, D. Hansel, and H. Sompolinsky, J. Comput. Neurosci. JCNEFR 0929-5313 10.1023/A:1008816611284 4, 57 (1997). (Pubitemid 27078020)
26. Z. P. Kilpatrick and P. C. Bressloff, Physica D PDNPDT 0167-2789 10.1016/j.physd.2009.06.003 239, 547 (2010).
27. W. C. Troy and V. Shusterman, SIAM J. Appl. Dyn. Syst. 1536-0040 10.1137/06066638X 6, 263 (2007).
28. S. Folias and P. Bressloff, SIAM J. Appl. Dyn. Syst. 1536-0040 10.1137/030602629 3, 378 (2004).
29. S. Coombes and M. R. Owen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.94.148102 94, 148102 (2005). (Pubitemid 40620451)
30. C. Laing, SIAM J. Appl. Dyn. Syst. 1536-0040 10.1137/040612890 4, 588 (2005). (Pubitemid 43385167)
31. S. E. Folias and P. C. Bressloff, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/040615171 65, 2067 (2005). (Pubitemid 41802091)
32. G. B. Ermentrout, J. Z. Jalics, and J. E. Rubin, SIAM J. Appl. Math. SMJMAP 0036-1399 10.1137/090775737 70, 3039 (2010).
33. S. Coombes and C. R. Laing, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.83.011912 83, 011912 (2011).
34. M. Rule, M. Stoffregen, and B. Ermentrout, PLoS Comput. Biol. 1553-734X 10.1371/journal.pcbi.1002158 7, e1002158 (2011).
35. V. A. Billock and B. H. Tsou, Proc. Natl. Acad. Sci. USA PNASA6 0027-8424 10.1073/pnas.0610813104 104, 8490 (2007). (Pubitemid 47175515)
36. B. J. Gluckman, H. Nguyen, S. L. Weinstein, and S. J. Schiff, J. Neurosci. 21, 590 (2001).
37. X. Han, X. Qian, J. G. Bernstein, H.-H. Zhou, G. T. Franzesi, P. Stern, R. T. Bronson, A. M. Graybiel, R. Desimone, and E. S. Boyden, Neuron NERNET 0896-6273 10.1016/j.neuron.2009.03.011 62, 191 (2009).
38. A. Mikhailov, L. Schimansky-Geier, and W. Ebeling, Phys. Lett. PYLAAG 0375-9601 10.1016/0375-9601(83)90163-9 96A, 453 (1983).
39. Y. Kawamura, H. Nakao, and Y. Kuramoto, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.84.046211 84, 046211 (2011).
40. X. Xie and M. A. Giese, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.65.051904 65, 051904 (2002). (Pubitemid 40606794)
41. H. Suarez, C. Koch, and R. Douglas, J. Neurosci. 15, 6700 (1995).
42. A. J. Watt, H. Cuntz, M. Mori, Z. Nusser, P. J. Sjostrom, and M. Hausser, Nature Neurosci. NANEFN 1097-6256 10.1038/nn.2285 12, 463 (2009).
43. H. V. Oviedo, I. Bureau, K. Svoboda, and A. M. Zador, Nature Neurosci. NANEFN 1097-6256 10.1038/nn.2659 13, 1413 (2010).
44. S. Coombes and M. R. Owen, SIAM J. Appl. Dyn. Syst. 1536-0040 10.1137/040605953 3, 574 (2004). (Pubitemid 40578317)
45. P. C. Bressloff and M. A. Webber (unpublished).
46. S. Coombes, G. J. Lord, and M. R. Owen, Physica D PDNPDT 0167-2789 10.1016/S0167-2789(03)00002-2 178, 219 (2003).
47. S. Coombes, C. R. Laing, H. Schmidt, N. Svanstedt, and J. A. Wyller, Discrete Cont. Dyn. Syst. Ser. A (to be published).
48. H. Schmidt, A. Hutt, and L. Schimansky-Geier, Physica D PDNPDT 0167-2789 10.1016/j.physd.2009.02.017 238, 1101 (2009).
49. Y. Kawamura, H. Nakao, K. Arai, H. Kori, and Y. Kuramoto, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.101.024101 101, 024101 (2008).
50. B. Ermentrout, Neural Comput. NEUCEB 0899-7667 10.1162/neco.1996.8.5.979 8, 979 (1996).
51. Z. P. Kilpatrick, S. E. Folias, and P. C. Bressloff, SIAM J. Appl. Dyn. Syst. 1536-0040 10.1137/070699214 7, 161 (2008).
52. W. C. Troy, SIAM J. Appl. Dyn. Syst. 1536-0040 10.1137/070709888 7, 1247 (2008).
53. M. Kamrunnahar, N. S. Dias, and S. J. Schiff, Ann. Biomed. Eng. ABMECF 0090-6964 10.1007/s10439-011-0248-y 39, 1482 (2011).
54. D. J. Pinto, R. K. Jackson, and C. E. Wayne, SIAM J. Appl. Dyn. Syst. 1536-0040 10.1137/040613020 4, 954 (2005). (Pubitemid 43385155)
55. L. Zhang, J. Diff. Eq. JDEQAK 0022-0396 10.1016/S0022-0396(03)00170-0 197, 162 (2004). (Pubitemid 38202747)
56. D. Hansel, G. Mato, and C. Meunier, Neural Comput. NEUCEB 0899-7667 10.1162/neco.1995.7.2.307 7, 307 (1995).
57. S. Coombes and M. R. Owen, in Fluids and Waves: Recent Trends in Applied Analysis, edited by, F. Botelho, T. Hagen, and, J. Jamison, AMS Contemporary Mathematics, Vol. 440 (AMS, Providence, RI, 2007), pp. 123-144.
58. Y. Lu, Y. Sato, and S.-I. Amari, Neural Comput. NEUCEB 0899-7667 10.1162/NECO-a-00111 23, 1248 (2011).
59. V. Shusterman and W. C. Troy, Phys. Rev. E PLEEE8 1539-3755 10.1103/PhysRevE.77.061911 77, 061911 (2008).
60. O. Feinerman, M. Segal, and E. Moses, J. Neurophysiol. JONEA4 0022-3077 10.1152/jn.00264.2005 94, 3406 (2005). (Pubitemid 41504777)