Controlling the onset of traveling pulses in excitable media by nonlocal spatial coupling and time-delayed feedback

Chaos

Volumn 19, Issue 1, 2009, Pages

  Schneider, Felix M ^a   Schöll, Eckehard ^a   Dahlem, Markus A ^a  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ACTION POTENTIAL; ANIMAL; BIOLOGICAL MODEL; BIOPHYSICS; BRAIN; COMPUTER SIMULATION; FEEDBACK SYSTEM; HUMAN; NERVE CELL; NERVE CELL NETWORK; NERVE CONDUCTION; PHYSIOLOGY; PROCEDURES; REPRODUCIBILITY; SYNAPTIC TRANSMISSION;

ACTION POTENTIALS; ANIMALS; BIOPHYSICS; BRAIN; COMPUTER SIMULATION; FEEDBACK; HUMANS; MODELS, BIOLOGICAL; MODELS, NEUROLOGICAL; NERVE NET; NEURAL CONDUCTION; NEURONS; REPRODUCIBILITY OF RESULTS; SYNAPTIC TRANSMISSION;

EID: 63849175283     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3096411     Document Type: Article

References (59)

1. Handbook of Chaos Control, edited by, E. Schöll, and, H. G. Schuster, (Wiley-VCH, Weinheim, 2008).
2. K. Pyragas, Phys. Lett. A 0375-9601 10.1016/0375-9601(92)90745-8 170, 421 (1992).
3. M. A. Dahlem, F. M. Schneider, and E. Schöll, Chaos 1054-1500 10.1063/1.2937120 18, 026110 (2008).
4. M. Kehrt, P. Hövel, V. Flunkert, M. A. Dahlem, P. Rodin, and E. Schöll, " Stabilization of complex spatio-temporal dynamics near a subcritical Hopf bifurcation by time-delayed feedback.," Eur. Phys. J. B (in press). 1434-6028
5. Y. N. Kyrychko, K. B. Blyuss, S. J. Hogan, and E. Schöll, " Control of spatio-temporal patterns in the Gray-Scott model.," Physica D (submitted). 0167-2789
6. K. A. Richardson, S. J. Schiff, and B. J. Gluckman, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.94.028103 94, 028103 (2005).
7. U. B. Barnikol, O. V. Popovych, C. Hauptmann, V. Sturm, H. J. Freund, and P. A. Tass, Philos. Trans. R. Soc. London, Ser. A 366, 3545 (2008).
8. M. Lauritzen, Brain 0006-8950 10.1093/brain/117.1.199 117, 199 (1994).
9. N. Hadjikhani and M. Sanchez Del, Proc. Natl. Acad. Sci. U.S.A. 0027-8424 10.1073/pnas.071582498 98, 4687 (2001).
10. M. Fabricius, S. Fuhr, R. Bhatia, M. Boutelle, P. Hashemi, A. J. Strong, and M. Lauritzen, Brain 0006-8950 10.1093/brain/awh716 129, 778 (2006).
11. M. A. Dahlem, F. M. Schneider, and E. Schöll, " Change of spatial excitability by gain controlled time-delayed feedback. " (unpublished).
12. B. Grafstein, in Brain Function: Cortical Excitability and Steady Potentials, edited by, M. A. B. Brazier, (University of California Press, Berkeley, 1963), pp. 87-124.
13. B. Lindner, J. García-Ojalvo, A. Neiman, and L. Schimansky-Geier, Phys. Rep. 0370-1573 10.1016/j.physrep.2003.10.015 392, 321 (2004).
14. G. B. Ermentrout, Rep. Prog. Phys. 0034-4885 10.1088/0034-4885/61/4/002 61, 353 (1998).
15. E. M. Izhikevich, Int. J. Bifurcation Chaos Appl. Sci. Eng. 0218-1274 10.1142/S0218127400000840 10, 1171 (2000).
16. A. T. Winfree, Chaos 1054-1500 10.1063/1.165844 1, 303 (1991).
17. Y. A. Kuznetsov, Elements of Applied Bifurcation Theory (Springer, New York, 1995).
18. M. A. Dahlem and S. C. Müller, Exp. Brain Res. 0014-4819 10.1007/PL00005700 115, 319 (1997).
19. A. T. Winfree, Science 0036-8075 10.1126/science.7973648 266, 1003 (1994).
20. A. S. Mikhailov and V. S. Zykov, Physica D 0167-2789 10.1016/0167- 2789(91)90134-U 52, 379 (1991).
21. Z. Nagy-Ungvarai, J. Ungvarai, and S. C. Müller, Chaos 1054-1500 10.1063/1.165973 3, 15 (1993).
22. M. Braune and H. Engel, Chem. Phys. Lett. 0009-2614 10.1016/0009-2614(93) 90005-L 204, 257 (1993).
23. J. Schlesner, V. Zykov, H. Engel, and E. Schöll, Phys. Rev. E 1063-651X 10.1103/PhysRevE.74.046215 74, 046215 (2006).
24. M. A. Dahlem and S. C. Müller, Ann. Phys. 0003-3804 10.1002/andp.200410087 13, 442 (2004).
25. M. A. Dahlem and N. Hadjikhani, " Migraine aura: retracting particle-like waves in weakly susceptible cortex.," PLoS ONE (in press). 1932-6203
26. T. Sakurai, E. Mihaliuk, F. Chirila, and K. Showalter, Science 0036-8075 10.1126/science.1071265 296, 2009 (2002).
27. V. S. Zykov and K. Showalter, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.94.068302 94, 068302 (2005).
28. A. S. Mikhailov and K. Showalter, Phys. Rep. 0370-1573 10.1016/j.physrep.2005.11.003 425, 79 (2006).
29. M. A. Dahlem, F. M. Schneider, and E. Schöll, J. Theor. Biol. 0022-5193 10.1016/j.jtbi.2007.11.019 251, 202 (2008).
30. F. Schlögl, Z. Phys. 0044-3328 10.1007/BF01379769 253, 147 (1972).
31. H. R. Wilson, Spikes, Decisions, and Actions: The Dynamical Foundations of Neuroscience (Oxford University Press, Oxford, 1999).
32. E. Schöll, Nonlinear Spatio-Temporal Dynamics and Chaos in Semiconductors (Cambridge University Press, Cambridge, 2001).
33. J. L. Hindmarsh and R. M. Rose, Nature (London) 0028-0836 10.1038/296162a0 296, 162 (1982).
34. K. F. Bonhoeffer, Naturwiss. 0028-1042 10.1007/BF00632438 40, 301 (1953).
35. R. FitzHugh, Biophys. J. 0006-3495 10.1016/S0006-3495(61)86902-6 1, 445 (1961).
36. J. Nagumo, S. Arimoto, and S. Yoshizawa, Proc. IRE 0096-8390 10.1109/JRPROC.1962.288235 50, 2061 (1962).
37. H. Kager, W. J. Wadman, and G. G. Somjen, J. Neurophysiol. 84, 495 (2000). 0022-3077
38. G. Florence, M. A. Dahlem, A. C. G. Almeida, J. W. M. Bassani, and J. Kurths, " The role of extracellular potassium dynamics in the different stages of ictal bursting and spreading depression: A computational study," J. Theor. Biol. (in press). 0022-5193
39. M. Gassel, E. Glatt, and F. Kaiser, Fluct. Noise Lett. 7, L225 (2007).
40. M. Gassel, E. Glatt, and F. Kaiser, Phys. Rev. E 1063-651X 10.1103/PhysRevE.77.066220 77, 066220 (2008).
41. This corrects Eq. (7) in Ref..
42. A. Hutt, Phys. Rev. E 1063-651X 10.1103/PhysRevE.70.052902 70, 052902 (2004).
43. B. Fiedler, V. Flunkert, M. Georgi, P. Hövel, and E. Schöll, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.98.114101 98, 114101 (2007).
44. T. Dahms, P. Hövel, and E. Schöll, Phys. Rev. E 1063-651X 10.1103/PhysRevE.76.056201 76, 056201 (2007).
45. P. C. Bressloff, Physica D 0167-2789 10.1016/S0167-2789(01)00266-4 155, 83 (2001).
46. M. A. Dahlem, G. Hiller, A. Panchuk, and E. Schöll, " Dynamics of delay-coupled excitable neural systems.," Int. J. Bifurcation Chaos Appl. Sci. Eng. (to be published), e-print arXiv:0803.2352. 0167-2789
47. E. Schöll, G. Hiller, P. Hövel, and M. A. Dahlem, Philos. Trans. R. Soc. London, Ser. A 367, 1079 (2009).
48. N. Manz, B. T. Ginn, and O. Steinbock, Phys. Rev. E 1063-651X 10.1103/PhysRevE.73.066218 73, 066218 (2006).
49. B. Sandstede, in Handbook of Dynamical Systems, edited by, B. Fiedler, (Elsevier/North-Holland, Amsterdam, 2002).
50. See this Focus Issue.
51. E. Ruppin, J. A. Reggia, and D. Glanzman, Prog. Brain Res. 121, ix (1999). 0079-6123
52. J. M. Davidenko, P. F. Kent, D. R. Chialvo, D. C. Michaels, and J. Jalife, Proc. Natl. Acad. Sci. U.S.A. 87, 8785 (1990). 0027-8424
53. P. Camacho and J. D. Lechleiter, Science 260, 226 (1993). 0036-8075
54. W. Lu, D. Yu, and R. G. Harrison, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.76.3316 76, 3316 (1996).
55. J. A. Reggia and D. Montgomery, Comput. Biol. Med. 0010-4825 10.1016/0010-4825(95)00051-8 26, 133 (1996).
56. A. J. Strong, J. Neurophysiol. 94, 5 (2005). 0022-3077
57. O. Herreras, J. Neurophysiol. 94, 3656 (2005). 0022-3077
58. M. Tinsley, J. Cui, F. V. Chirila, A. Taylor, S. Zhong, and K. Showalter, Phys. Rev. Lett. 0031-9007 10.1103/PhysRevLett.95.038306 95, 038306 (2005).
59. B. E. Shapiro, J. Comput. Neurosci. 0929-5313 10.1023/A:1008924227961 10, 99 (2001).