메뉴 건너뛰기




Volumn 15, Issue 7, 2005, Pages 2283-2293

Pattern formation in small arrays of locally coupled oscillators

Author keywords

Coupled oscillators; Pattern formation; Spiral waves

Indexed keywords


EID: 24144480079     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127405013150     Document Type: Article
Times cited : (6)

References (42)
  • 1
    • 4243665470 scopus 로고
    • Euclidean symmetry and the dynamics of rotating spiral waves
    • Barkley, D. [1994] "Euclidean symmetry and the dynamics of rotating spiral waves," Phys. Rev. Lett. 72, 164-167.
    • (1994) Phys. Rev. Lett. , vol.72 , pp. 164-167
    • Barkley, D.1
  • 3
    • 0035534589 scopus 로고    scopus 로고
    • Interaction of spiral waves and checkerboard patterns in a two-dimensional coupled circle-map lattice
    • Chung, T. & Kim, S. [2001] "Interaction of spiral waves and checkerboard patterns in a two-dimensional coupled circle-map lattice," J. Korean Phys. Soc. 38, 550-553.
    • (2001) J. Korean Phys. Soc. , vol.38 , pp. 550-553
    • Chung, T.1    Kim, S.2
  • 4
    • 0000747853 scopus 로고
    • Frequency plateaus in a chain of weakly coupled oscillators, I
    • Ermentrout, B. & Kopell, N. [1984] "Frequency plateaus in a chain of weakly coupled oscillators, I," SIAM J. Math. Anal. 15, 215-237.
    • (1984) SIAM J. Math. Anal. , vol.15 , pp. 215-237
    • Ermentrout, B.1    Kopell, N.2
  • 5
    • 0022364842 scopus 로고
    • The behavior of rings of coupled oscillators
    • Ermentrout, B. [1985] "The behavior of rings of coupled oscillators," J. Math. Biol. 23, 55-74.
    • (1985) J. Math. Biol. , vol.23 , pp. 55-74
    • Ermentrout, B.1
  • 6
    • 0027103530 scopus 로고
    • Stable periodic solutions to discrete and continuum arrays of weakly coupled nonlinear oscillators
    • Ermentrout, B. [1992] "Stable periodic solutions to discrete and continuum arrays of weakly coupled nonlinear oscillators," SIAM J. Appl. Math. 52, 1665-1687.
    • (1992) SIAM J. Appl. Math. , vol.52 , pp. 1665-1687
    • Ermentrout, B.1
  • 7
    • 0013533004 scopus 로고
    • A heuristic description of spiral wave instability in discrete media
    • Ermentrout, B. [1995] "A heuristic description of spiral wave instability in discrete media," Physica D82, 154-164.
    • (1995) Physica , vol.D82 , pp. 154-164
    • Ermentrout, B.1
  • 8
    • 0001104658 scopus 로고    scopus 로고
    • Neural networks as spatio-temporal pattern-forming systems
    • Ermentrout, B. [1998] "Neural networks as spatio-temporal pattern-forming systems," Rep. Progr. Phys. 61, 353-430.
    • (1998) Rep. Progr. Phys. , vol.61 , pp. 353-430
    • Ermentrout, B.1
  • 9
    • 0000530394 scopus 로고    scopus 로고
    • Meandering of the spiral tip: An alternative approach
    • Golubitsky, M., LeBlanc, V. & Melbourne, I. [1997] "Meandering of the spiral tip: An alternative approach," Nonlin. Sci. 7, 557-586.
    • (1997) Nonlin. Sci. , vol.7 , pp. 557-586
    • Golubitsky, M.1    LeBlanc, V.2    Melbourne, I.3
  • 12
    • 0001645343 scopus 로고
    • Spiral waves in reaction-diffusion equations
    • Hagan, P. [1982] "Spiral waves in reaction-diffusion equations," SIAM J. Appl. Math. 42, 762-786.
    • (1982) SIAM J. Appl. Math. , vol.42 , pp. 762-786
    • Hagan, P.1
  • 13
    • 4243706164 scopus 로고    scopus 로고
    • Theory of spiral wave dynamics in weakly excitable media: Asymptotic reduction to a kinematic model and applications
    • Hakim, V. & Karma, A. [1999] "Theory of spiral wave dynamics in weakly excitable media: Asymptotic reduction to a kinematic model and applications," Phys. Rev. E60, 5073-5105.
    • (1999) Phys. Rev. , vol.E60 , pp. 5073-5105
    • Hakim, V.1    Karma, A.2
  • 14
    • 33845184582 scopus 로고
    • Chemical vortex dynamics in the Belousov-Zhabotinsky reaction and in the two-variable Oregonator model
    • Jahnke, W., Skaggs, W. & Winfree, A. [1989] "Chemical vortex dynamics in the Belousov-Zhabotinsky reaction and in the two-variable Oregonator model," J. Phys. Chem. 93, 740-749.
    • (1989) J. Phys. Chem. , vol.93 , pp. 740-749
    • Jahnke, W.1    Skaggs, W.2    Winfree, A.3
  • 15
    • 0000039189 scopus 로고
    • A survey of spiralwave behavior in the Oregonator model
    • Jahnke, W. & Winfree, A. [1991] "A survey of spiralwave behavior in the Oregonator model," Int. J. Bifurcation and Chaos 1, 445-466.
    • (1991) Int. J. Bifurcation and Chaos , vol.1 , pp. 445-466
    • Jahnke, W.1    Winfree, A.2
  • 16
    • 0038090710 scopus 로고
    • Rotating spiral waves in reaction-diffusion systems
    • Koga, S. [1982] "Rotating spiral waves in reaction-diffusion systems," Prog. Theor. Phys. 67, 164-178.
    • (1982) Prog. Theor. Phys. , vol.67 , pp. 164-178
    • Koga, S.1
  • 17
    • 84990585743 scopus 로고
    • Symmetry and phaselocking in chains of weakly coupled oscillators
    • Kopell, N. & Ermentrout, B. [1986] "Symmetry and phaselocking in chains of weakly coupled oscillators," Commun. Pure Appl. Math. 39, 623-660.
    • (1986) Commun. Pure Appl. Math. , vol.39 , pp. 623-660
    • Kopell, N.1    Ermentrout, B.2
  • 18
    • 0025477416 scopus 로고
    • Phase transitions and other phenomena in chains of coupled oscillators
    • Kopell, N. & Ermentrout, B. [1990] "Phase transitions and other phenomena in chains of coupled oscillators," SIAM J. Appl. Math. 50, 1014-1052.
    • (1990) SIAM J. Appl. Math. , vol.50 , pp. 1014-1052
    • Kopell, N.1    Ermentrout, B.2
  • 20
    • 0041407010 scopus 로고    scopus 로고
    • Translational symmetry-breaking for spiral waves
    • LeBlanc, V. & Wulff, C. [2000] "Translational symmetry-breaking for spiral waves," J. Nonlin. Sci. 10, 569-601.
    • (2000) J. Nonlin. Sci. , vol.10 , pp. 569-601
    • LeBlanc, V.1    Wulff, C.2
  • 21
    • 0025567093 scopus 로고
    • Synchronization of pulse coupled oscillators
    • Mirollo, R. & Strogatz, S. [1990] "Synchronization of pulse coupled oscillators," SIAM J. Appl. Math. 50, 1645-1662.
    • (1990) SIAM J. Appl. Math. , vol.50 , pp. 1645-1662
    • Mirollo, R.1    Strogatz, S.2
  • 22
    • 0028151850 scopus 로고
    • Simple and complex spiral wave dynamics
    • Müller, S. & Zykov, V. [1994] "Simple and complex spiral wave dynamics," Phil. Trans. R. Soc. London A347, 677-685.
    • (1994) Phil. Trans. R. Soc. London , vol.A347 , pp. 677-685
    • Müller, S.1    Zykov, V.2
  • 23
    • 41349093107 scopus 로고    scopus 로고
    • Regular and chaotic phase synchronization of coupled circle maps
    • Osipov, G. & Kurths, J. [2001] "Regular and chaotic phase synchronization of coupled circle maps," Phys. Rev. E65, 016216.
    • (2001) Phys. Rev. , vol.E65 , pp. 016216
    • Osipov, G.1    Kurths, J.2
  • 24
    • 0037017186 scopus 로고    scopus 로고
    • Phase synchronization of chaotic rotators
    • Osipov, G., Pikovsky, A. & Kurths, J. [2002] "Phase synchronization of chaotic rotators," Phys. Rev. Lett. 88, 054102.
    • (2002) Phys. Rev. Lett. , vol.88 , pp. 054102
    • Osipov, G.1    Pikovsky, A.2    Kurths, J.3
  • 25
    • 0028714868 scopus 로고
    • Stable rotating waves in two-dimensional discrete active media
    • Paullet, J. & Ermentrout, B. [1994] "Stable rotating waves in two-dimensional discrete active media," SIAM J. Appl. Math. 54, 1720-1744.
    • (1994) SIAM J. Appl. Math. , vol.54 , pp. 1720-1744
    • Paullet, J.1    Ermentrout, B.2
  • 28
    • 0032353077 scopus 로고    scopus 로고
    • Monotonicity of phaselocked solutions in chains and arrays of nearest-neighbor coupled oscillators
    • Ren, L. & Ermentrout, B. [1998] "Monotonicity of phaselocked solutions in chains and arrays of nearest-neighbor coupled oscillators," SIAM J. Math. Anal. 29, 208-234.
    • (1998) SIAM J. Math. Anal. , vol.29 , pp. 208-234
    • Ren, L.1    Ermentrout, B.2
  • 29
    • 0039592732 scopus 로고    scopus 로고
    • Phaselocking in chains of multiple-coupled oscillators
    • Ren, L. & Ermentrout, B. [2000] "Phaselocking in chains of multiple-coupled oscillators," Physica D143, 56-73.
    • (2000) Physica , vol.D143 , pp. 56-73
    • Ren, L.1    Ermentrout, B.2
  • 30
    • 0001098827 scopus 로고
    • Local and global entrainments in oscillator lattices
    • Sakaguchi, H., Shinomoto, S. & Kuramoto, Y. [1987] "Local and global entrainments in oscillator lattices," Prog. Theor. Phys. 77, 1005-1010.
    • (1987) Prog. Theor. Phys. , vol.77 , pp. 1005-1010
    • Sakaguchi, H.1    Shinomoto, S.2    Kuramoto, Y.3
  • 31
    • 0000575665 scopus 로고
    • Mutual entrainment in oscillator lattices with non-variational type interaction
    • Sakaguchi, H., Shinomoto, S. & Kuramoto, Y. [1988] "Mutual entrainment in oscillator lattices with non-variational type interaction," Prog. Theor. Phys. 79, 1069-1079.
    • (1988) Prog. Theor. Phys. , vol.79 , pp. 1069-1079
    • Sakaguchi, H.1    Shinomoto, S.2    Kuramoto, Y.3
  • 32
    • 0001091987 scopus 로고
    • Motions of spiral waves in oscillatory media and in the presence of obstacles
    • Sepulchre, J. & Babloyantz, A. [1993] "Motions of spiral waves in oscillatory media and in the presence of obstacles," Phys. Rev. E48, 187-195.
    • (1993) Phys. Rev. , vol.E48 , pp. 187-195
    • Sepulchre, J.1    Babloyantz, A.2
  • 33
    • 33744852947 scopus 로고
    • Periodic to quasiperiodic transition of chemical spiral rotation
    • Skinner, G. & Swinney, H. [1990] "Periodic to quasiperiodic transition of chemical spiral rotation," Physica D48, 1-16.
    • (1990) Physica , vol.D48 , pp. 1-16
    • Skinner, G.1    Swinney, H.2
  • 34
    • 0039592729 scopus 로고    scopus 로고
    • From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators
    • Strogatz, S. [2000] "From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators," Physica D143, 1-20.
    • (2000) Physica , vol.D143 , pp. 1-20
    • Strogatz, S.1
  • 36
    • 0032482432 scopus 로고    scopus 로고
    • Collective dynamics of small world networks
    • Watts, D. & Strogatz, S. [1998] "Collective dynamics of small world networks," Nature 393, 440-442.
    • (1998) Nature , vol.393 , pp. 440-442
    • Watts, D.1    Strogatz, S.2
  • 37
    • 0002260042 scopus 로고
    • Three-dimensional chemical waves in the Belousov-Zhabotinskii reaction
    • Welsh, B., Gomatam, J. & Burgess, A. [1983] "Three-dimensional chemical waves in the Belousov-Zhabotinskii reaction," Nature 304, 611-614.
    • (1983) Nature , vol.304 , pp. 611-614
    • Welsh, B.1    Gomatam, J.2    Burgess, A.3
  • 38
    • 0001620105 scopus 로고
    • Scroll-shaped waves of chemical activity in three dimensions
    • Winfree, A. [1973] "Scroll-shaped waves of chemical activity in three dimensions," Science 181, 937-939.
    • (1973) Science , vol.181 , pp. 937-939
    • Winfree, A.1
  • 40
    • 33749361692 scopus 로고
    • Varieties of spiral wave behavior: An experimentalist's approach to the theory of excitable media
    • Winfree, A. [1991] "Varieties of spiral wave behavior: An experimentalist's approach to the theory of excitable media," Chaos 1, 303-334.
    • (1991) Chaos , vol.1 , pp. 303-334
    • Winfree, A.1
  • 41
    • 0036739701 scopus 로고    scopus 로고
    • Chemical waves and fibrillating hearts: Discovery by computation
    • Winfree, A. [2002] "Chemical waves and fibrillating hearts: Discovery by computation," J. Biosci. 27, 465-473.
    • (2002) J. Biosci. , vol.27 , pp. 465-473
    • Winfree, A.1
  • 42
    • 0030258439 scopus 로고    scopus 로고
    • Spiral waves on circular and spherical domains of excitable medium
    • Zykov, V. &: Müller, S. [1996] "Spiral waves on circular and spherical domains of excitable medium," Physica A97, 322-332.
    • (1996) Physica , vol.A97 , pp. 322-332
    • Zykov, V.1    Müller, S.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.