Nucleation of reaction-diffusion waves on curved surfaces

New Journal of Physics

Volumn 16, Issue , 2014, Pages

  Kneer, Frederike ^a   Schöll, Eckehard ^a   Dahlem, Markus A ^b  

^a TECHNISCHE UNIVERSITÄT BERLIN   (Germany)

^b HUMBOLDT UNIVERSITY   (Germany)

Author keywords

Gaussian curvature; localized structures; pattern formation; reaction diffusion

Indexed keywords

EID: 84900392400     PISSN: 13672630     EISSN: None     Source Type: Journal    
DOI: 10.1088/1367-2630/16/5/053010     Document Type: Article

References (40)

1. Dahlem M A and Tusch J 2012 Predicted selective increase of cortical magnification due to cortical folding. J. Math. Neurosci 2 14
2. Karatas H, Erdener S E, Gursoy-Ozdemir Y, Lule S, Eren-Kocak E, Sen Z D and Dalkara T 2013 Spreading depression triggers headache by activating neuronal Panx1 channels Science 339 1092-5
3. Dreier J P 2011 The role of spreading depression, spreading depolarization and spreading ischemia in neurological disease Nat. Med. 17 439-47
4. Dahlem M A and Hadjikhani N 2009 Migraine aura: retracting particle-like waves in weakly susceptible cortex PLoS ONE 4 e5007
5. Dahlem M A, Graf R, Strong A J, Dreier J P, Dahlem Y A, Sieber M, Hanke W, Podoll K and Schöll E 2010 Two-dimensional wave patterns of spreading depolarization: retracting, re-entrant, and stationary waves Physica D 239 889-903
6. Krischer K and Mikhailov A S 1994 Bifurcation to traveling spots in reaction-diffusion systems Phys. Rev. Lett. 73 3165-8 (Pubitemid 24976183)
7. Bode M and Purwins H G 1995 Pattern formation in reaction-diffusion systems-dissipative solitons in physical systems Physica D 86 53
8. Schenk C P, Or-Guil M, Bode M and Purwins H G 1997 Interacting pulses in three-component reaction-diffusion systems on two-dimensional domains Phys. Rev. Lett. 78 3781
9. Kim M, Bertram M, Pollmann M, von Oertzen A, Mikhailov A S, Rotermund H H and Ertl G 2001 Controlling chemical turbulence by global delayed feedback: pattern formation in catalytic CO oxidation on Pt(110) Science 292 1357 (Pubitemid 32476218)
10. Zykov V S, Bordiougov G, Brandtstädter H, Gerdes I and Engel H 2004 Global control of spiral wave dynamics in an excitable domain of circular and elliptical shape Phys. Rev. Lett. 92 018304
11. Schlesner J, Zykov V, Engel H and Schöll E 2006 Stabilization of unstable rigid rotation of spiral waves in excitable media Phys. Rev. E 74 046215 (Pubitemid 44631306)
12. Mikhailov A S and Showalter K 2006 Control of waves, patterns and turbulence in chemical systems Phys. Rep. 425 79-194 (Pubitemid 43174943)
13. Dahlem M A, Schneider F M and Schöll E 2008 Failure of feedback as a putative common mechanism of spreading depolarizations in migraine and stroke Chaos 18 026110
14. Schneider F M, Schöll E and Dahlem M A 2009 Controlling the onset of traveling pulses in excitable media by nonlocal spatial coupling and time delayed feedback Chaos 19 015110
15. Kyrychko Y N, Blyuss K B, Hogan S J and Schöll E 2009 Control of spatio-temporal patterns in the Gray-Scott model Chaos 19 043126
16. Maselko J and Showalter K 1989 Chemical waves on spherical surfaces Nature 339 609-11
17. Abramychev A Yu, Davydov V A and Zykov V S 1990 Drift of spiral waves on nonuniformly curved surfaces J. Exp. Theor. Phys. 70 666
18. Davydov V A and Zykov V S 1991 Kinematics of spiral waves on nonuniformly curved surfaces Physica. D 49 71-74
19. Davydov V A and Zykov V S 1993 Spiral autowaves in a round excitable medium J. Exp. Theor. Phys. 76 414-9
20. Mikhailov A S, Davydov V A and Zykov V S 1994 Complex dynamics of spiral waves and motion of curves Physica D 70 1-39
21. Davydov V A, Manz N, Steinbock O, Zykov V S and Müller S C 2000 Excitation fronts on a periodically modulated curved surface Phys. Rev. Lett. 85 868-71
22. Davydov V A, Morozov V G and Davydov N V 2000 Ring-shaped autowaves on curved surfaces Phys. Lett. A 267 326-30
23. Davydov V A, Manz N, Steinbock O and Müller S C 2002 Critical properties of excitation waves on curved surfaces: curvature-dependent loss of excitability Europhys. Lett. 59 344-50
24. Manz N, Davydov V A, C Müller S and Bär M 2003 Dependence of the spiral rotation frequency on the surface curvature of reaction-diffusion systems Phys. Lett. A 316 311-6
25. Lindner B, García-Ojalvo J, Neiman A and Schimansky-Geier L 2004 Effects of noise in excitable systems Phys. Rep. 392 321-424 (Pubitemid 38231071)
26. van der Pol B 1926 On relaxation oscillations Phil. Mag. 2 978-92
27. Bonhoeffer K F 1948 Activation of passive iron as a model for the excitation of nerve J. Gen. Physiol 32 69-91
28. Bonhoeffer K F 1953 Modelle der Nervenerregung Naturwissenschaften 40 301-11
29. FitzHugh R 1961 Impulses and physiological states in theoretical models of nerve membrane Biophys. J. 1 445-66
30. Nagumo J, Arimoto S and Yoshizawa S 1962 An active pulse transmission line simulating nerve axon Proc. IRE 50 2061-70
31. Hodgkin A L and Huxley A F 1952 A quantitative description of membrane current and its application to conduction and excitation in nerve J. Physiol. 117 500
32. Dahlem M A and Müller S C 2004 Reaction-diffusion waves in neuronal tissue and the window of cortical excitability Ann. Phys. 13 442-9
33. Hübel N, Schöll E and Dahlem M A 2014 Bistable dynamics underlying excitability of ion homeostasis in ion-based neuron models PLoS Comp. Biol. at press (arXiv:1310.1941v1).
34. Winfree A T 1991 Varieties of spiral wave behaviour: an experimentalist's approach to the theory of excitable media Chaos 1 303-34
35. Kühnel W 2005 Differentialgeometrie (Wiesbaden: Vieweg)
36. Davydov V A, Morozov V G and Davydov N V 2003 Critical properties of autowaves propagating on deformed cylindrical surfaces Phys. Lett. A 307 265-8
37. Krupa M, Sandstede B and Szmolyan P 1997 Fast and slow waves in the FitzHugh-Nagumo equation J. Differ. Equ. 133 49-97 (Pubitemid 127164522)
38. Zykov V S 1984 Simulation of Wave Processes in Excitable Media (Moscow: Wiley) (Engl. transl. from 1992)
39. Moon P and Spencer D E 1971 Field Theory Handbook 2nd edn (Berlin: Springer)
40. Kosugi T 2013 Electronic properties and persistent spin currents of nanospring under static magnetic field J. Phys. Soc. Japan 531 173-99