Periodic travelling wave (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Periodic travelling wave" in English language version.

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aps.org

link.aps.org

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archive.today

  • S. A. Gourley, N. F. Britton (1993) "Instability of traveling wave solutions of a population model with nonlocal effects", IMA J. Appl. Math. 51: 299–310. DOI:10.1093/imamat/51.3.299
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brown.edu

dam.brown.edu

cam.ac.uk

damtp.cam.ac.uk

doi.org

dx.doi.org

  • S. Coombes (2001) "From periodic travelling waves to travelling fronts in the spike-diffuse-spike model of dendritic waves", Math. Biosci. 170: 155–172. DOI:10.1016/S0025-5564(00)00070-5
  • J.A. Sherratt, G. J. Lord (2007) "Nonlinear dynamics and pattern bifurcations in a model for vegetation stripes in semi-arid environments", Theor. Popul. Biol. 71 (2007): 1–11. DOI:10.1016/j.tpb.2006.07.009
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  • J. A. Sherratt (1994) "Irregular wakes in reaction-diffusion waves", Physica D 70: 370–382. DOI:10.1016/0167-2789(94)90072-8
  • S.V. Petrovskii, H. Malchow (1999) "A minimal model of pattern formation in a prey–predator system", Math. Comp. Modelling 29: 49–63. DOI:10.1016/S0895-7177(99)00070-9
  • J.D.M. Rademacher, B. Sandstede, A. Scheel (2007) "Computing absolute and essential spectra using continuation", Physica D 229: 166–183. DOI:10.1016/j.physd.2007.03.016
  • M. J. Smith, J. D. M. Rademacher, J. A. Sherratt (2009) "Absolute stability of wavetrains can explain spatiotemporal dynamics in reaction-diffusion systems of lambda-omega type", SIAM J. Appl. Dyn. Systems 8: 1136–1159. DOI:10.1137/090747865
  • K. Maginu (1981) "Stability of periodic travelling wave solutions with large spatial periods in reaction-diffusion systems", J. Diff. Eqns. 39: 73–99. 10.1016/0022-0396(81)90084-X
  • M. J. Smith, J.A. Sherratt (2007) "The effects of unequal diffusion coefficients on periodic travelling waves in oscillatory reaction-diffusion systems", Physica D 236: 90–103. DOI:10.1016/j.physd.2007.07.013
  • B. Sandstede, A. Scheel (2000) "Absolute and convective instabilities of waves on unbounded and large bounded domains", Physica D 145: 233–277. DOI:10.1016/S0167-2789(00)00114-7
  • A. L. Kay, J. A. Sherratt (2000) "Spatial noise stabilizes periodic wave patterns in oscillatory systems on finite domains", SIAM J. Appl. Math. 61: 1013–1041. DOI:10.1137/S0036139999360696
  • M. Ipsen, L. Kramer, P.G. Sorensen (2000) "Amplitude equations for description of chemical reaction–diffusion systems", Phys. Rep. 337: 193–235. DOI:10.1016/S0370-1573(00)00062-4
  • A.S. Mikhailov, K. Showalter (2006) "Control of waves, patterns and turbulence in chemical systems", Phys. Rep. 425: 79–194. DOI:10.1016/j.physrep.2005.11.003
  • S.V. Petrovskii, H. Malchow (2001) "Wave of chaos: new mechanism of pattern formation in spatio-temporal population dynamics", Theor. Pop. Biol. 59: 157–174. DOI:10.1006/tpbi.2000.1509
  • M. R. Garvie, M. Golinski (2010) "Metapopulation dynamics for spatially extended predator–prey interactions", Ecological Complexity 7: 55–59. DOI:10.1016/j.ecocom.2009.05.001
  • J. A. Sherratt (1994) "On the evolution of periodic plane waves in reaction-diffusion equations of λ-ω type", SIAM J. Appl. Math. 54: 1374–1385. DOI: 10.1137/S0036139993243746
  • N. Bekki, K. Nozaki (1985) "Formations of spatial patterns and holes in the generalized Ginzburg–Landau equation", Phys. Lett. A 110: 133–135. DOI: 10.1016/0375-9601(85)90759-5
  • J. A. Sherratt (2003)"Periodic travelling wave selection by Dirichlet boundary conditions in oscillatory reaction-diffusion systems", SIAM J. Appl. Math. 63: 1520–1538. DOI:10.1137/S0036139902392483
  • J. Lega (2001) "Traveling hole solutions of the complex Ginzburg–Landau equation: a review", Physica D 152: 269–287. DOI:10.1016/S0167-2789(01)00174-9
  • B. Deconinck, J. N. Kutz (2006) "Computing spectra of linear operators using the Floquet–Fourier–Hill method", J. Comput. Phys. 219: 296–321. DOI:10.1016/j.jcp.2006.03.020
  • J.A. Sherratt (2012) "Numerical continuation methods for studying periodic travelling wave (wavetrain) solutions of partial differential equations", Appl. Math. Computation 218: 4684–4694. DOI:10.1016/j.amc.2011.11.005
  • R. Moss, D.A. Elston, A. Watson (2000) "Spatial asynchrony and demographic travelling waves during red grouse population cycles", Ecology 81: 981-989. DOI:10.1890/0012-9658
  • C. Valentin, J. M. d'Herbes, J. Poesen (1999) "Soil and water components of banded vegetation patterns", Catena 37: 1-24. DOI:10.1016/S0341-8162(99)00053-3
  • D. L. Dunkerley, K. J. Brown (2002) "Oblique vegetation banding in the Australian arid zone: implications for theories of pattern evolution and maintenance", J. Arid Environ. 52: 163–181. DOI:10.1006/jare.2001.0940
  • G. Bordyugov, N. Fischer, H. Engel, N. Manz, O. Steinbock (2010) "Anomalous dispersion in the Belousov–Zhabotinsky reaction: experiments and modeling", Physica D 239: 766–775. DOI:10.1016/j.physd.2009.10.022

nature.com

  • E. Ranta, V. Kaitala (1997) "Travelling waves in vole population dynamics", Nature 390: 456. DOI:10.1038/37261

pnas.org

  • J.A. Sherratt, M. A. Lewis, A. C. Fowler (1995) "Ecological chaos in the wake of invasion", Proc. Natl. Acad. Sci. USA 92: 2524–2528. 10.1073/pnas.92.7.2524

royalsocietypublishing.org

rspb.royalsocietypublishing.org

  • X. Lambin, D. A. Elston, S. J. Petty, J. L. MacKinnon (1998) "Spatial asynchrony and periodic travelling waves in cyclic populations of field voles", Proc. R. Soc. Lond. B 265: 1491–1496. DOI:10.1098/rspb.1998.0462
  • J. A. Sherratt, X. Lambin, C. J. Thomas, T. N. Sherratt (2002) "Generation of periodic waves by landscape features in cyclic predator-prey systems" Proc. R. Soc. Lond. B 269: 327–334. DOI:10.1098/rspb.2001.1890

rspa.royalsocietypublishing.org

  • M. Sieber, H. Malchow, S.V. Petrovskii (2010) "Noise-induced suppression of periodic travelling waves in oscillatory reaction–diffusion systems", Proc. R. Soc. Lond. A 466: 1903–1917. DOI:10.1098/rspa.2009.0611

science.org

  • M. Rietkerk, S.C. Dekker, P.C. de Ruiter, J. van de Koppel (2004) "Self-organized patchiness and catastrophic shifts in ecosystems", Science 305: 1926–1929.DOI:10.1126/science.1101867
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springer.com

link.springer.com

  • P. Ashwin, M. V. Bartuccelli, T. J. Bridges, S. A. Gourley (2002) "Travelling fronts for the KPP equation with spatio-temporal delay", Z. Angew. Math. Phys. 53: 103–122. DOI:0010-2571/02/010103-20
  • D. M. Johnson, O. N. Bjornstad, A.M. Liebhold (2006) "Landscape mosaic induces travelling waves of insect outbreaks", Oecologia 148: 51–60. DOI:10.1007/s00442-005-0349-0
  • J. A. Sherratt (2013) "Numerical continuation of boundaries in parameter space between stable and unstable periodic travelling wave (wavetrain) solutions of partial differential equations", Adv. Comput. Math, in press. DOI:10.1007/s10444-012-9273-0
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ulb.ac.be

theses.ulb.ac.be

  • V. Deblauwe (2010) "Modulation des structures de vegetation auto-organisees en milieu aride / Self-organized vegetation pattern modulation in arid climates". PhD thesis, Universite Libre de Bruxelles."Catalogue des thèses électroniques de l'ULB - Thèse ULBetd-04122010-093151". Archived from the original on 2013-09-27. Retrieved 2013-01-09.

web.archive.org

  • Section 3.4.2 of B. Sandstede (2002) "Stability of travelling waves". In: B. Fiedler (ed.) Handbook of Dynamical Systems II, North-Holland, Amsterdam, pp. 983–1055. http://www.dam.brown.edu/people/sandsted/publications/survey-stability-of-waves.pdf Archived 2013-09-27 at the Wayback Machine
  • V. Deblauwe (2010) "Modulation des structures de vegetation auto-organisees en milieu aride / Self-organized vegetation pattern modulation in arid climates". PhD thesis, Universite Libre de Bruxelles."Catalogue des thèses électroniques de l'ULB - Thèse ULBetd-04122010-093151". Archived from the original on 2013-09-27. Retrieved 2013-01-09.

wiley.com

onlinelibrary.wiley.com

  • A. C. Nilssen, O. Tenow, H. Bylund (2007) "Waves and synchrony in Epirrita autumnata/Operophtera brumata outbreaks II. Sunspot activity cannot explain cyclic outbreaks", J. Animal Ecol. 76: 269–275. DOI:10.1111/j.1365-2656.2006.01205.x/full