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Volumn 63, Issue 5, 2003, Pages 1520-1538

Periodic travelling wave selection by dirichlet boundary conditions in oscillatory reaction-diffusion systems

Author keywords

Oscillatory systems; Periodic waves; Reaction diffusion; Wavetrains

Indexed keywords

BOUNDARY CONDITIONS; COMPUTER SIMULATION; DIFFUSION; MATHEMATICAL MODELS; ORDINARY DIFFERENTIAL EQUATIONS; WAVE EQUATIONS;

EID: 0242404009     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0036139902392483     Document Type: Article
Times cited : (24)

References (38)
  • 2
    • 0017068359 scopus 로고
    • Bifurcation analysis of reaction-diffusion equations. III. Chemical oscillations
    • J. F. G. AUCHMUTY AND G. NICOLIS (1976), Bifurcation analysis of reaction-diffusion equations. III. Chemical oscillations, Bull. Math. Biol., 38, pp. 325-350.
    • (1976) Bull. Math. Biol. , vol.38 , pp. 325-350
    • Auchmuty, J.F.G.1    Nicolis, G.2
  • 3
    • 0033231663 scopus 로고    scopus 로고
    • Spatial population dynamics: Analyzing patterns and processes of population synchrony
    • O. N. BJøRNSTAD, R. A. IMS, AND X. LAMBIN (1999), Spatial population dynamics: Analyzing patterns and processes of population synchrony, Trends in Ecology and Evolution, 14, pp. 427-432.
    • (1999) Trends in Ecology and Evolution , vol.14 , pp. 427-432
    • Bjørnstad, O.N.1    Ims, R.A.2    Lambin, X.3
  • 5
    • 0004603310 scopus 로고
    • Stable small amplitude solutions in reaction-diffusion systems
    • G. B. ERMENTROUT (1981), Stable small amplitude solutions in reaction-diffusion systems, Quart. Appl. Math., 39, pp. 61-86.
    • (1981) Quart. Appl. Math. , vol.39 , pp. 61-86
    • Ermentrout, G.B.1
  • 6
    • 0001505194 scopus 로고    scopus 로고
    • Transition fronts and localised structures in bistable reaction-diffusion equations
    • G. B. ERMENTROUT, X. CHEN, AND Z. CHEN (1997), Transition fronts and localised structures in bistable reaction-diffusion equations, Phys. D, 108, pp. 147-167.
    • (1997) Phys. D , vol.108 , pp. 147-167
    • Ermentrout, G.B.1    Chen, X.2    Chen, Z.3
  • 7
    • 0000747853 scopus 로고
    • Frequency plateaus in a chain of weakly coupled oscillators
    • G. B. ERMENTROUT AND N. KOPELL (1984), Frequency plateaus in a chain of weakly coupled oscillators, I, SIAM J. Math. Anal., 15, pp. 215-237.
    • (1984) I, SIAM J. Math. Anal. , vol.15 , pp. 215-237
    • Ermentrout, G.B.1    Kopell, N.2
  • 8
    • 84990585743 scopus 로고
    • Symmetry and phase-locking in chains of weakly coupled oscillators
    • G. B. ERMENTROUT AND N. KOPELL (1986), Symmetry and phase-locking in chains of weakly coupled oscillators, Commun. Pure Appl. Anal., 49, pp. 623-660.
    • (1986) Commun. Pure Appl. Anal. , vol.49 , pp. 623-660
    • Ermentrout, G.B.1    Kopell, N.2
  • 10
    • 0000031199 scopus 로고
    • Target patterns in reaction-diffusion systems
    • P. S. HAGAN (1981a), Target patterns in reaction-diffusion systems, Adv. Appl. Math., 2, pp. 400-416.
    • (1981) Adv. Appl. Math. , vol.2 , pp. 400-416
    • Hagan, P.S.1
  • 11
    • 0344845499 scopus 로고
    • The instability of non-monotonic wave solutions of parabolic equations
    • P. S. HAGAN (1981b), The instability of non-monotonic wave solutions of parabolic equations, Stud. Appl. Math., 64, pp. 57-88.
    • (1981) Stud. Appl. Math. , vol.64 , pp. 57-88
    • Hagan, P.S.1
  • 13
    • 84990652766 scopus 로고
    • On the nonlinear stability of plane waves for the Ginzburg-Landau equation
    • T. KAPITULA (1994), On the nonlinear stability of plane waves for the Ginzburg-Landau equation, Comm. Pure Appl. Math., 47, pp. 831-841.
    • (1994) Comm. Pure Appl. Math. , vol.47 , pp. 831-841
    • Kapitula, T.1
  • 14
    • 0033353519 scopus 로고    scopus 로고
    • On the persistence of spatiotemporal oscillations generated by invasion
    • A. L. KAY AND J. A. SHERRATT (1999), On the persistence of spatiotemporal oscillations generated by invasion, IMA J. Appl. Math., 63, pp. 199-216.
    • (1999) IMA J. Appl. Math. , vol.63 , pp. 199-216
    • Kay, A.L.1    Sherratt, J.A.2
  • 15
    • 0034912178 scopus 로고    scopus 로고
    • Spatial noise stabilizes periodic wave patterns in oscillatory systems on finite domains
    • A. L. KAY AND J. A. SHERRATT (2000), Spatial noise stabilizes periodic wave patterns in oscillatory systems on finite domains, SIAM J. Appl. Math., 61, pp. 1013-1041.
    • (2000) SIAM J. Appl. Math. , vol.61 , pp. 1013-1041
    • Kay, A.L.1    Sherratt, J.A.2
  • 16
    • 0004522182 scopus 로고
    • Target pattern solutions to reaction-diffusion equations in the presence of impurities
    • N. KOPELL (1981), Target pattern solutions to reaction-diffusion equations in the presence of impurities, Adv. Appl. Math., 2, pp. 389-399.
    • (1981) Adv. Appl. Math. , vol.2 , pp. 389-399
    • Kopell, N.1
  • 17
    • 0000588222 scopus 로고
    • Plane wave solutions to reaction-diffusion equations
    • N. KOPELL AND L. N. HOWARD (1973), Plane wave solutions to reaction-diffusion equations, Stud. Appl. Math., 52, pp. 291-328.
    • (1973) Stud. Appl. Math. , vol.52 , pp. 291-328
    • Kopell, N.1    Howard, L.N.2
  • 18
    • 0013141409 scopus 로고
    • Target patterns and horseshoes from a perturbed central force problem: Some temporally periodic solutions to reaction-diffusion problems
    • N. KOPELL AND L. N. HOWARD (1981), Target patterns and horseshoes from a perturbed central force problem: Some temporally periodic solutions to reaction-diffusion problems, Stud. Appl. Math., 64, pp. 1-56.
    • (1981) Stud. Appl. Math. , vol.64 , pp. 1-56
    • Kopell, N.1    Howard, L.N.2
  • 20
    • 0032558265 scopus 로고    scopus 로고
    • Spatial asynchrony and periodic travelling waves in cyclic populations of field voles
    • X. LAMBIN, D. A. ELSTON, S. J. PETTY, AND J. L. MACKINNON (1998), Spatial asynchrony and periodic travelling waves in cyclic populations of field voles, Proc. Roy. Soc. London Ser. B, 265, pp. 1491-1496.
    • (1998) Proc. Roy. Soc. London Ser. B , vol.265 , pp. 1491-1496
    • Lambin, X.1    Elston, D.A.2    Petty, S.J.3    MacKinnon, J.L.4
  • 22
    • 0003062258 scopus 로고
    • Stability of periodic travelling wave solutions with large spatial periods in reaction-diffusion systems
    • K. MAGINU (1981), Stability of periodic travelling wave solutions with large spatial periods in reaction-diffusion systems, J. Differential Equations, 39, pp. 73-99.
    • (1981) J. Differential Equations , vol.39 , pp. 73-99
    • Maginu, K.1
  • 23
    • 0033924233 scopus 로고    scopus 로고
    • Spatial asynchrony and demographic travelling waves during red grouse population cycles
    • R. Moss, D. A. ELSTON, AND A. WATSON (2000), Spatial asynchrony and demographic travelling waves during red grouse population cycles, Ecology, 81, pp. 981-989.
    • (2000) Ecology , vol.81 , pp. 981-989
    • Moss, R.1    Elston, D.A.2    Watson, A.3
  • 24
    • 0000374910 scopus 로고
    • Target patterns and pacemakers in a reaction-diffusion system
    • H. NAGASHIMA (1991), Target patterns and pacemakers in a reaction-diffusion system, J. Phys. Soc. Japan, 60, pp. 2797-2799.
    • (1991) J. Phys. Soc. Japan , vol.60 , pp. 2797-2799
    • Nagashima, H.1
  • 25
    • 0039440566 scopus 로고    scopus 로고
    • A two parameter family of travelling waves with a singular barrier arising from the modelling of matrix mediated malignant invasion
    • A. J. PERUMPANANI, J. NORBURY, J. A. SHERRATT, AND H. M. BYRNE (1999), A two parameter family of travelling waves with a singular barrier arising from the modelling of matrix mediated malignant invasion, Phys. D, 126, pp. 145-159.
    • (1999) Phys. D , vol.126 , pp. 145-159
    • Perumpanani, A.J.1    Norbury, J.2    Sherratt, J.A.3    Byrne, H.M.4
  • 26
    • 0033120656 scopus 로고    scopus 로고
    • A minimal model of pattern formation in a prey predator system
    • S. V. PETROVSKII AND H. MALCHOW (1999), A minimal model of pattern formation in a prey predator system, Math. Comput. Modelling, 29, pp. 49-63.
    • (1999) Math. Comput. Modelling , vol.29 , pp. 49-63
    • Petrovskii, S.V.1    Malchow, H.2
  • 27
    • 0034147519 scopus 로고    scopus 로고
    • Critical phenomena in plankton communities: KISS model revisited
    • S. V. PETROVSKII AND H. MALCHOW (2000), Critical phenomena in plankton communities: KISS model revisited, Nonlinear Anal. Real World Appl., 1, pp. 37-51.
    • (2000) Nonlinear Anal. Real World Appl. , vol.1 , pp. 37-51
    • Petrovskii, S.V.1    Malchow, H.2
  • 28
    • 0034471753 scopus 로고    scopus 로고
    • Lotka-Volterra equations with chemotaxis: Walls, barriers and travelling waves
    • G. J. PETTET, D. L. McELWAIN, AND J. NORBURY (2000), Lotka-Volterra equations with chemotaxis: Walls, barriers and travelling waves, IMA J. Math. Appl. Med. Biol., 17, pp. 395-413.
    • (2000) IMA J. Math. Appl. Med. Biol. , vol.17 , pp. 395-413
    • Pettet, G.J.1    McElwain, D.L.2    Norbury, J.3
  • 29
    • 0032353077 scopus 로고    scopus 로고
    • Monotonicity of phaselocked solutions in chains and arrays of nearest-neighbor coupled oscillators
    • L. REN AND G. B. ERMENTROUT (1998), Monotonicity of phaselocked solutions in chains and arrays of nearest-neighbor coupled oscillators, SIAM J. Math. Anal., 29, pp. 208-234.
    • (1998) SIAM J. Math. Anal. , vol.29 , pp. 208-234
    • Ren, L.1    Ermentrout, G.B.2
  • 30
    • 0034541090 scopus 로고    scopus 로고
    • Symmetries, periodic plane waves and blow-up of lambda-omega systems
    • J. L. ROMERO, M. L. GANDARIAS, AND E. MEDINA (2000), Symmetries, periodic plane waves and blow-up of lambda-omega systems, Phys. D, 147, pp. 259-272.
    • (2000) Phys. D , vol.147 , pp. 259-272
    • Romero, J.L.1    Gandarias, M.L.2    Medina, E.3
  • 32
    • 0028518381 scopus 로고
    • On the evolution of periodic plane waves in reaction-diffusion systems of λ-ω type
    • J. A. SHERRATT (1994a), On the evolution of periodic plane waves in reaction-diffusion systems of λ-ω type, SIAM J. Appl. Math., 54, pp. 1374-1385.
    • (1994) SIAM J. Appl. Math. , vol.54 , pp. 1374-1385
    • Sherratt, J.A.1
  • 33
    • 0001049459 scopus 로고
    • Irregular wakes in reaction-diffusion waves
    • J. A. SHERRATT (1994b), Irregular wakes in reaction-diffusion waves, Phys. D, 70, pp. 370-384.
    • (1994) Phys. D , vol.70 , pp. 370-384
    • Sherratt, J.A.1
  • 35
    • 53149140283 scopus 로고    scopus 로고
    • Generation of periodic waves by landscape features in cyclic predator-prey systems
    • J. A. SHERRATT, X. LAMBIN, C. J. THOMAS, AND T. N. SHERRATT (2002), Generation of periodic waves by landscape features in cyclic predator-prey systems, Proc. Roy. Soc. London Ser. B, 269, pp. 327-334.
    • (2002) Proc. Roy. Soc. London Ser. B , vol.269 , pp. 327-334
    • Sherratt, J.A.1    Lambin, X.2    Thomas, C.J.3    Sherratt, T.N.4
  • 36
    • 0033780796 scopus 로고    scopus 로고
    • Application of coupled oscillator models to understand extensive synchrony domains and travelling waves in populations of the field vole in Kielder forest, UK
    • T. N. SHERRATT, X. LAMBIN, S. J. PETTY, J. L. MACKINNON, C. F. COLES, AND C. J. THOMAS (2000), Application of coupled oscillator models to understand extensive synchrony domains and travelling waves in populations of the field vole in Kielder forest, UK, J. Appl. Ecol., 37, pp. 148-158.
    • (2000) J. Appl. Ecol. , vol.37 , pp. 148-158
    • Sherratt, T.N.1    Lambin, X.2    Petty, S.J.3    Mackinnon, J.L.4    Coles, C.F.5    Thomas, C.J.6
  • 37
    • 0031075937 scopus 로고    scopus 로고
    • On the propagation of calcium waves in an inhomogeneous medium
    • J. SNEYD AND J. SHERRATT (1997), On the propagation of calcium waves in an inhomogeneous medium, SIAM J. Appl. Math., 57, pp. 73-94.
    • (1997) SIAM J. Appl. Math. , vol.57 , pp. 73-94
    • Sneyd, J.1    Sherratt, J.2


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