메뉴 건너뛰기




Volumn 10, Issue 1, 2000, Pages 69-101

Hopf bifurcation from rotating waves and patterns in physical space

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0038074690     PISSN: 09388974     EISSN: None     Source Type: Journal    
DOI: 10.1007/s003329910004     Document Type: Article
Times cited : (51)

References (46)
  • 1
    • 0022677808 scopus 로고
    • Flow regimes in a circular Couette system with independently rotating cylinders
    • C.D. Andereck, S.S. Liu, and H.L. Swinney. Flow regimes in a circular Couette system with independently rotating cylinders. J. Fluid Mech. 164 (1986) 155-183.
    • (1986) J. Fluid Mech. , vol.164 , pp. 155-183
    • Andereck, C.D.1    Liu, S.S.2    Swinney, H.L.3
  • 2
    • 23544474504 scopus 로고
    • A model for fast computer-simulation of waves in excitable media
    • D. Barkley. A model for fast computer-simulation of waves in excitable media. Physica D 49 (1991) 61-70.
    • (1991) Physica D , vol.49 , pp. 61-70
    • Barkley, D.1
  • 3
    • 4243665470 scopus 로고
    • Euclidean symmetry and the dynamics of rotating spiral waves
    • D. Barkley. Euclidean symmetry and the dynamics of rotating spiral waves. Phys. Rev. Lett. 72 (1994) 165-167.
    • (1994) Phys. Rev. Lett. , vol.72 , pp. 165-167
    • Barkley, D.1
  • 4
    • 4243682358 scopus 로고
    • Spiral-wave dynamics in a simple model of excitable media: The transition from simple to compound rotation
    • D. Barkley, M. Kness, and L. S. Tuckerman. Spiral-wave dynamics in a simple model of excitable media: The transition from simple to compound rotation. Phys. Rev. A 42 (1990) 2489-2492.
    • (1990) Phys. Rev. A , vol.42 , pp. 2489-2492
    • Barkley, D.1    Kness, M.2    Tuckerman, L.S.3
  • 5
    • 0026846050 scopus 로고
    • Nonlinear dynamics of cellular flames
    • A. Bayliss and B.J. Matkowsky. Nonlinear dynamics of cellular flames. SIAM J. Appl. Math. 52 (1992) 396-415.
    • (1992) SIAM J. Appl. Math. , vol.52 , pp. 396-415
    • Bayliss, A.1    Matkowsky, B.J.2
  • 6
    • 0001885308 scopus 로고
    • Structure and dynamics of modulated traveling waves in cellular flames
    • A. Bayliss, B.J. Matkowsky, and H. Riecke. Structure and dynamics of modulated traveling waves in cellular flames. Physica D 74 (1994) 1-23.
    • (1994) Physica D , vol.74 , pp. 1-23
    • Bayliss, A.1    Matkowsky, B.J.2    Riecke, H.3
  • 7
    • 0040782325 scopus 로고
    • Symmetries in modulated traveling waves in combustion: Jumping ponies on a merry-go-round
    • Pattern Formation: Symmetry Methods and Applications (J. Chadam and W. Langford eds.), AMS, Providence, RI
    • A. Bayliss, B.J. Matkowsky, and H. Riecke. Symmetries in modulated traveling waves in combustion: jumping ponies on a merry-go-round. Pattern Formation: Symmetry Methods and Applications (J. Chadam and W. Langford eds.), Fields Institute Communications 5, AMS, Providence, RI, 1995, 19-43.
    • (1995) Fields Institute Communications , vol.5 , pp. 19-43
    • Bayliss, A.1    Matkowsky, B.J.2    Riecke, A.H.3
  • 8
    • 0001878629 scopus 로고
    • Primary and secondary bifurcations in the Couette-Taylor problem
    • P. Chossat and G. Iooss. Primary and secondary bifurcations in the Couette-Taylor problem. Japan J. Appl. Math. 2 No. 1 (1985) 37-68.
    • (1985) Japan J. Appl. Math. , vol.2 , Issue.1 , pp. 37-68
    • Chossat, P.1    Iooss, G.2
  • 9
    • 0026807080 scopus 로고
    • Modulated waves in Taylor-Couette flow. Part 1
    • K.T. Coughlin and P.S. Marcus. Modulated waves in Taylor-Couette flow. Part 1. Analysis J. Fluid Mech. 234 (1992) 1-18. Part 2. Numerical simulation, ibid.19-46.
    • (1992) Analysis J. Fluid Mech. , vol.234 , pp. 1-18
    • Coughlin, K.T.1    Marcus, P.S.2
  • 10
    • 0026807080 scopus 로고
    • Part 2. Numerical simulation
    • K.T. Coughlin and P.S. Marcus. Modulated waves in Taylor-Couette flow. Part 1. Analysis J. Fluid Mech. 234 (1992) 1-18. Part 2. Numerical simulation, ibid.19-46.
    • (1992) Analysis J. Fluid Mech. , vol.234 , pp. 19-46
  • 12
    • 0000384434 scopus 로고    scopus 로고
    • Bifurcation from relative equilibria of noncompact group actions: Skew products, meanders and drifts
    • B. Fiedler, B. Sandstede, A. Scheel, and C. Wulff. Bifurcation from relative equilibria of noncompact group actions: skew products, meanders and drifts. Documenta Math. 1 (1996) 479-505.
    • (1996) Documenta Math. , vol.1 , pp. 479-505
    • Fiedler, B.1    Sandstede, B.2    Scheel, A.3    Wulff, C.4
  • 13
    • 0010050153 scopus 로고    scopus 로고
    • Normal forms, resonances, and meandering tip motions near relative equilibria of Euclidean group actions
    • B. Fiedler and D. Turaev. Normal forms, resonances, and meandering tip motions near relative equilibria of Euclidean group actions. Arch. Rational Mech. & Anal. 165 (1998) 129-159.
    • (1998) Arch. Rational Mech. & Anal. , vol.165 , pp. 129-159
    • Fiedler, B.1    Turaev, D.2
  • 14
    • 0000530394 scopus 로고    scopus 로고
    • Meandering of the spiral tip: An alternative approach
    • M. Golubitsky, V.G. LeBlanc, and I. Melbourne. Meandering of the spiral tip: an alternative approach. J. Nonlin. Sci. 7 (1997) 557-586.
    • (1997) J. Nonlin. Sci. , vol.7 , pp. 557-586
    • Golubitsky, M.1    Leblanc, V.G.2    Melbourne, I.3
  • 15
    • 0021853542 scopus 로고
    • Hopf bifurcation in the presence of symmetry
    • M. Golubitsky and I.N. Stewart. Hopf bifurcation in the presence of symmetry. Arch. Rational Mech. & Anal. 87 No. 2 (1985) 107-165.
    • (1985) Arch. Rational Mech. & Anal. , vol.87 , Issue.2 , pp. 107-165
    • Golubitsky, M.1    Stewart, I.N.2
  • 16
    • 0003147711 scopus 로고
    • Singularities and groups in bifurcation theory: Vol. II
    • Springer-Verlag, New York
    • M. Golubitsky, I. Stewart, and D. Schaeffer. Singularities and Groups in Bifurcation Theory: Vol. II, Applied Mathematical Sciences 69, Springer-Verlag, New York, 1988.
    • (1988) Applied Mathematical Sciences , vol.69
    • Golubitsky, M.1    Stewart, I.2    Schaeffer, D.3
  • 17
    • 85037511562 scopus 로고    scopus 로고
    • M. Gorman. Private communication.
    • M. Gorman. Private communication.
  • 19
    • 0005865480 scopus 로고    scopus 로고
    • Ratcheting motion of concentric rings in cellular flames
    • M. Gorman, M. el-Hamdi, and K.A. Robbins. Ratcheting motion of concentric rings in cellular flames. Phys. Rev. Lett. 76 (1996) 228-231.
    • (1996) Phys. Rev. Lett. , vol.76 , pp. 228-231
    • Gorman, M.1    El-Hamdi, M.2    Robbins, K.A.3
  • 21
    • 0040187825 scopus 로고
    • Visual observation of the second characteristic mode in a quasiperiodic flow
    • M. Gorman and H.L. Swinney. Visual observation of the second characteristic mode in a quasiperiodic flow. Phys. Rev. Lett. 43 (1980) 1871-1875.
    • (1980) Phys. Rev. Lett. , vol.43 , pp. 1871-1875
    • Gorman, M.1    Swinney, H.L.2
  • 22
    • 84974199028 scopus 로고
    • Spatial and temporal characteristics of modulated waves in the circular Couette system
    • M. Gorman and H.L. Swinney. Spatial and temporal characteristics of modulated waves in the circular Couette system. J. Fluid Mech. 117 (1982) 123-142.
    • (1982) J. Fluid Mech. , vol.117 , pp. 123-142
    • Gorman, M.1    Swinney, H.L.2
  • 23
    • 0039596577 scopus 로고
    • Doubly periodic circular Couette flow: Experiments compared with predictions from dynamics and symmetry
    • M. Gorman, H.L. Swinney, and D. Rand. Doubly periodic circular Couette flow: experiments compared with predictions from dynamics and symmetry. Phys. Rev. Lett 46 (1981) 992-995.
    • (1981) Phys. Rev. Lett , vol.46 , pp. 992-995
    • Gorman, M.1    Swinney, H.L.2    Rand, D.3
  • 25
    • 33845184582 scopus 로고
    • Chemical vortex dynamics in the Belousov-Zhabotinsky reaction and in the two-variable oregonator model
    • W. Jahnke, W.E. Skaggs, and A.T. Winfree. Chemical vortex dynamics in the Belousov-Zhabotinsky reaction and in the two-variable Oregonator model. J. Phys. Chem. 93 (1989) 740-749.
    • (1989) J. Phys. Chem. , vol.93 , pp. 740-749
    • Jahnke, W.1    Skaggs, W.E.2    Winfree, A.T.3
  • 26
    • 0000039189 scopus 로고
    • A survey of spiral-wave behaviors in the oregonator model
    • W. Jahnke and A.T. Winfree. A survey of spiral-wave behaviors in the Oregonator model. Int. J. Bifur. & Chaos 1 (1991) 445-466.
    • (1991) Int. J. Bifur. & Chaos , vol.1 , pp. 445-466
    • Jahnke, W.1    Winfree, A.T.2
  • 28
    • 0001103998 scopus 로고
    • Bifurcations of relative equilibria
    • M. Krupa. Bifurcations of relative equilibria. SIAM J. Math. Anal. 21 (1990) 1453-1486.
    • (1990) SIAM J. Math. Anal. , vol.21 , pp. 1453-1486
    • Krupa, M.1
  • 29
    • 44949280120 scopus 로고
    • Direction-reversing traveling waves
    • A.S. Landsberg and E. Knobloch. Direction-reversing traveling waves. Phys. Lett. A 159 (1991) 17-20.
    • (1991) Phys. Lett. A , vol.159 , pp. 17-20
    • Landsberg, A.S.1    Knobloch, E.2
  • 30
    • 0001248698 scopus 로고    scopus 로고
    • Transition from simple rotating chemical spirals to meandering and traveling spirals
    • G. Li, Q. Ouyang, V. Petrov, and H.L. Swinney. Transition from simple rotating chemical spirals to meandering and traveling spirals. Phys. Rev. Lett. 77 (1996) 2105-2108.
    • (1996) Phys. Rev. Lett. , vol.77 , pp. 2105-2108
    • Li, G.1    Ouyang, Q.2    Petrov, V.3    Swinney, H.L.4
  • 31
    • 0024913032 scopus 로고
    • Analysis of meandering in Zykov kinetics
    • E. Lugosi. Analysis of meandering in Zykov kinetics. Physica D 40 (1989) 331-337.
    • (1989) Physica D , vol.40 , pp. 331-337
    • Lugosi, E.1
  • 32
    • 0021500531 scopus 로고
    • Simulation of Taylor-Couette flow. Part 2. Numerical results for wavy-vortex flow with one travelling wave
    • P.S. Marcus. Simulation of Taylor-Couette flow. Part 2. Numerical results for wavy-vortex flow with one travelling wave. J. Fluid Mech. 146 (1984) 65-113.
    • (1984) J. Fluid Mech. , vol.146 , pp. 65-113
    • Marcus, P.S.1
  • 33
    • 0033196120 scopus 로고    scopus 로고
    • Modal decomposition of hopping states in cellular flames
    • A. Palacios, M. Gorman, and G.H. Gunaratne. Modal decomposition of hopping states in cellular flames. Chaos 9 (1999) 755-767.
    • (1999) Chaos , vol.9 , pp. 755-767
    • Palacios, A.1    Gorman, M.2    Gunaratne, G.H.3
  • 34
    • 0242449865 scopus 로고    scopus 로고
    • Cellular pattern formation in circular domains
    • A. Palacios, G.H. Gunaratne, M. Gorman, and K.A. Robbins. Cellular pattern formation in circular domains. Chaos 7 (3) (1997) 463-475.
    • (1997) Chaos , vol.7 , Issue.3 , pp. 463-475
    • Palacios, A.1    Gunaratne, G.H.2    Gorman, M.3    Robbins, K.A.4
  • 35
    • 0000325432 scopus 로고    scopus 로고
    • Core dynamics of multi-armed spirals in Rayleigh-Bénard convection
    • B.B. Plapp and E. Bodenschatz. Core dynamics of multi-armed spirals in Rayleigh-Bénard convection. Physica Scripta 67 (1996) 111-117.
    • (1996) Physica Scripta , vol.67 , pp. 111-117
    • Plapp, B.B.1    Bodenschatz, E.2
  • 36
    • 0020002828 scopus 로고
    • Dynamics and symmetry. Predictions for modulated waves in rotating fluids
    • D. Rand. Dynamics and symmetry. Predictions for modulated waves in rotating fluids. Arch. Rational Mech. & Anal. 79 (1982) 1-38.
    • (1982) Arch. Rational Mech. & Anal. , vol.79 , pp. 1-38
    • Rand, D.1
  • 37
    • 0020002824 scopus 로고
    • Bifurcation from rotating waves
    • M. Renardy. Bifurcation from rotating waves. Arch. Rational Mech. & Anal. 79 (1982) 49-84.
    • (1982) Arch. Rational Mech. & Anal. , vol.79 , pp. 49-84
    • Renardy, M.1
  • 39
    • 0031581236 scopus 로고    scopus 로고
    • Dynamics of spiral waves in unbounded domains using center-manifold reductions
    • B. Sandstede, A. Scheel, and C. Wulff. Dynamics of spiral waves in unbounded domains using center-manifold reductions. J. Diff. Eqns. 141 (1997) 122-149.
    • (1997) J. Diff. Eqns. , vol.141 , pp. 122-149
    • Sandstede, B.1    Scheel, A.2    Wulff, C.3
  • 40
    • 33744852947 scopus 로고
    • Periodic to quasiperiodic transition of chemical spiral rotation
    • G.S. Skinner and H.L. Swinney. Periodic to quasiperiodic transition of chemical spiral rotation. Physica D 48 (1991) 1-16.
    • (1991) Physica D , vol.48 , pp. 1-16
    • Skinner, G.S.1    Swinney, H.L.2
  • 41
    • 0001700505 scopus 로고
    • Stability of a viscous liquid contained between two rotating cylinders
    • G.I. Taylor. Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. Roy. Soc. London A 223 (1923) 289-343.
    • (1923) Phil. Trans. Roy. Soc. London A , vol.223 , pp. 289-343
    • Taylor, G.I.1
  • 42
    • 0000764751 scopus 로고
    • The geometry of biological time
    • Springer, New York
    • A.T. Winfree. The Geometry of Biological Time. Biomathematics 8, Springer, New York, 1980.
    • (1980) Biomathematics , vol.8
    • Winfree, A.T.1
  • 44
    • 0040782316 scopus 로고
    • Nonpropogating oscillatory modes in Couette-Taylor flow
    • L.-H. Zhang and H.L. Swinney. Nonpropogating oscillatory modes in Couette-Taylor flow. Phys. Rev. A 31 (1985) 1006-1009.
    • (1985) Phys. Rev. A , vol.31 , pp. 1006-1009
    • Zhang, L.-H.1    Swinney, H.L.2
  • 45
    • 0000539073 scopus 로고
    • Cycloidal circulation of spiral waves in an excitable medium
    • V.S. Zykov. Cycloidal circulation of spiral waves in an excitable medium. Biofizika 31 (1986) 862-865.
    • (1986) Biofizika , vol.31 , pp. 862-865
    • Zykov, V.S.1
  • 46
    • 0040187819 scopus 로고
    • Kinematics of nonstationary circulation of spiral waves in an excitable medium
    • V.S. Zykov. Kinematics of nonstationary circulation of spiral waves in an excitable medium. Biofizika 32 (1987) 337-340.
    • (1987) Biofizika , vol.32 , pp. 337-340
    • Zykov, V.S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.