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Volumn 17, Issue 6, 2007, Pages 505-525

On the diffusive nicholson's blowflies equation with nonlocal delay

Author keywords

Nicholson's blowflies model; Nonlocal delay; Reaction diffusion; Travelling wave front

Indexed keywords


EID: 84867942512     PISSN: 09388974     EISSN: 14321467     Source Type: Journal    
DOI: 10.1007/s00332-007-9003-9     Document Type: Article
Times cited : (111)

References (39)
  • 1
    • 33750189759 scopus 로고    scopus 로고
    • Travelling wave-fronts for generalized Fisher equations with spatio-temporal delays
    • 1113.34024 10.1016/j.jde.2006.08.015 2281191
    • S. Ai 2007 Travelling wave-fronts for generalized Fisher equations with spatio-temporal delays J. Differ. Equ. 232 104 133 1113.34024 10.1016/j.jde.2006.08.015 2281191
    • (2007) J. Differ. Equ. , vol.232 , pp. 104-133
    • Ai, S.1
  • 2
    • 0036003046 scopus 로고    scopus 로고
    • Travelling fronts for the KPP equation with spatio-temporal delay
    • 1005.92024 10.1007/s00033-002-8145-8 1889183
    • P.B. 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 1005.92024 10.1007/s00033-002-8145-8 1889183
    • (2002) Z. Angew. Math. Phys. , vol.53 , pp. 103-122
    • Ashwin, P.B.1    Bartuccelli, M.V.2    Bridges, T.J.3    Gourley, S.A.4
  • 3
    • 0009677529 scopus 로고    scopus 로고
    • Sufficient conditions for stability of linear differential equations with distributed delay
    • 0993.34065
    • S. Bernard J. Bélair M.C. Mackey 2001 Sufficient conditions for stability of linear differential equations with distributed delay Discret. Contin. Dyn. Syst. Ser. B 1 233 256 0993.34065
    • (2001) Discret. Contin. Dyn. Syst. Ser. B , vol.1 , pp. 233-256
    • Bernard, S.1    Bélair, J.2    MacKey, M.C.3
  • 4
    • 0346040342 scopus 로고    scopus 로고
    • Dynamics of a strongly nonlocal reaction-diffusion population model
    • 1050.35038 10.1088/0951-7715/17/1/018 2023445
    • J. Billingham 2004 Dynamics of a strongly nonlocal reaction-diffusion population model Nonlinearity 17 313 346 1050.35038 10.1088/0951-7715/17/1/018 2023445
    • (2004) Nonlinearity , vol.17 , pp. 313-346
    • Billingham, J.1
  • 5
    • 0021438024 scopus 로고
    • The dynamics of population models with distributed maturation periods
    • 0532.92020 10.1016/0040-5809(84)90011-X 752482
    • S.P. Blythe R.M. Nisbet W.S.C. Gurney 1984 The dynamics of population models with distributed maturation periods Theor. Popul. Biol. 25 289 311 0532.92020 10.1016/0040-5809(84)90011-X 752482
    • (1984) Theor. Popul. Biol. , vol.25 , pp. 289-311
    • Blythe, S.P.1    Nisbet, R.M.2    Gurney, W.S.C.3
  • 6
    • 0000579765 scopus 로고
    • Stability switches in distributed delay models
    • 0589.92018 10.1016/0022-247X(85)90158-1 802903
    • S.P. Blythe R.M. Nisbet W.S.C. Gurney N. MacDonald 1985 Stability switches in distributed delay models J. Math. Anal. Appl. 109 388 396 0589.92018 10.1016/0022-247X(85)90158-1 802903
    • (1985) J. Math. Anal. Appl. , vol.109 , pp. 388-396
    • Blythe, S.P.1    Nisbet, R.M.2    Gurney, W.S.C.3    MacDonald, N.4
  • 7
    • 0024965270 scopus 로고
    • Aggregation and the competitive exclusion principle
    • 10.1016/S0022-5193(89)80189-4 976118
    • N.F. Britton 1989 Aggregation and the competitive exclusion principle J. Theor. Biol. 136 57 66 10.1016/S0022-5193(89)80189-4 976118
    • (1989) J. Theor. Biol. , vol.136 , pp. 57-66
    • Britton, N.F.1
  • 8
    • 0025545718 scopus 로고
    • Spatial structures and periodic travelling waves in an integro-deferential reaction-diffusion population model
    • 0723.92019 10.1137/0150099 1080515
    • N.F. Britton 1990 Spatial structures and periodic travelling waves in an integro-deferential reaction-diffusion population model SIAM J. Appl. Math. 50 1663 1688 0723.92019 10.1137/0150099 1080515
    • (1990) SIAM J. Appl. Math. , vol.50 , pp. 1663-1688
    • Britton, N.F.1
  • 9
    • 0022890422 scopus 로고
    • Traveling waves in diffusive predator-prey equations: Periodic orbits and point-to periodic heteroclinic orbits
    • 0617.92020 10.1137/0146063 866281
    • S. Dunbar 1986 Traveling waves in diffusive predator-prey equations: Periodic orbits and point-to periodic heteroclinic orbits SIAM J. Appl. Math. 46 1057 1078 0617.92020 10.1137/0146063 866281
    • (1986) SIAM J. Appl. Math. , vol.46 , pp. 1057-1078
    • Dunbar, S.1
  • 10
    • 33745891805 scopus 로고    scopus 로고
    • Nonmonotone traveling waves in a single species reaction-diffusion equation with delay
    • 05058346 10.1016/j.jde.2006.05.006 2254435
    • T. Faria S. Trofimchuk 2006 Nonmonotone traveling waves in a single species reaction-diffusion equation with delay J. Differ. Equ. 228 357 376 05058346 10.1016/j.jde.2006.05.006 2254435
    • (2006) J. Differ. Equ. , vol.228 , pp. 357-376
    • Faria, T.1    Trofimchuk, S.2
  • 11
    • 0033752098 scopus 로고    scopus 로고
    • Travelling fronts in the diffusive Nicholson's blowflies equation with distributed delays
    • 0969.35133 10.1016/S0895-7177(00)00175-8 1792102
    • S.A. Gourley 2000 Travelling fronts in the diffusive Nicholson's blowflies equation with distributed delays Math. Comput. Model. 32 843 853 0969.35133 10.1016/S0895-7177(00)00175-8 1792102
    • (2000) Math. Comput. Model. , vol.32 , pp. 843-853
    • Gourley, S.A.1
  • 12
    • 38249004015 scopus 로고
    • On a modified Volterra population equation with diffusion
    • 0805.35062 10.1016/0362-546X(93)90082-4 1237130
    • S.A. Gourley N.F. Britton 1993 On a modified Volterra population equation with diffusion Nonlinear Anal. 21 389 395 0805.35062 10.1016/0362-546X(93) 90082-4 1237130
    • (1993) Nonlinear Anal. , vol.21 , pp. 389-395
    • Gourley, S.A.1    Britton, N.F.2
  • 13
    • 1542616886 scopus 로고    scopus 로고
    • Wavefronts and global stability in a time-delayed population model with stage structure
    • 1047.92037 1994271 10.1098/rspa.2002.1094
    • S.A. Gourley Y. Kuang 2003 Wavefronts and global stability in a time-delayed population model with stage structure Proc. R. Soc. Lond. Ser. A 459 1563 1579 1047.92037 1994271 10.1098/rspa.2002.1094
    • (2003) Proc. R. Soc. Lond. Ser. A , vol.459 , pp. 1563-1579
    • Gourley, S.A.1    Kuang, Y.2
  • 14
    • 23044524588 scopus 로고    scopus 로고
    • Dynamics of the diffusive Nicholson's blowflies equation with distributed delays
    • 0973.34064 10.1017/S0308210500000688 1809104
    • S.A. Gourley S. Ruan 2000 Dynamics of the diffusive Nicholson's blowflies equation with distributed delays Proc. R. Soc. Edinburgh Sect. A 130 1275 1291 0973.34064 10.1017/S0308210500000688 1809104
    • (2000) Proc. R. Soc. Edinburgh Sect. A , vol.130 , pp. 1275-1291
    • Gourley, S.A.1    Ruan, S.2
  • 15
    • 2442624461 scopus 로고    scopus 로고
    • Convergence and travelling fronts in functional differential equations with nonlocal terms: A competition model
    • 1040.92045 10.1137/S003614100139991 2048407
    • S.A. Gourley S. Ruan 2003 Convergence and travelling fronts in functional differential equations with nonlocal terms: A competition model SIAM J. Math. Anal. 35 806 822 1040.92045 10.1137/S003614100139991 2048407
    • (2003) SIAM J. Math. Anal. , vol.35 , pp. 806-822
    • Gourley, S.A.1    Ruan, S.2
  • 16
    • 33845515570 scopus 로고    scopus 로고
    • Delayed non-local diffusive systems in biological invasion and disease spread
    • Fields Institute Communications H. Brunner X.-Q. Zhao X. Zou (eds). Am. Math. Soc. Providence
    • Gourley, S.A., Wu, J.: Delayed non-local diffusive systems in biological invasion and disease spread. In: Brunner, H., Zhao, X.-Q., Zou, X. (eds.) Nonlinear Dynamics and Evolution Equations. Fields Institute Communications, vol. 48, pp. 137-200. Am. Math. Soc., Providence (2006)
    • (2006) Nonlinear Dynamics and Evolution Equations , vol.48 , pp. 137-200
    • Gourley, S.A.1    Wu, J.2
  • 17
    • 0035384407 scopus 로고    scopus 로고
    • Spatio-temporal pattern formation in a nonlocal reaction-diffusion equation
    • 0988.35082 10.1080/14689360116914 1835994
    • S.A. Gourley M.A.J. Chaplain F.A. Davidson 2001 Spatio-temporal pattern formation in a nonlocal reaction-diffusion equation Dyn. Syst. 16 173 192 0988.35082 10.1080/14689360116914 1835994
    • (2001) Dyn. Syst. , vol.16 , pp. 173-192
    • Gourley, S.A.1    Chaplain, M.A.J.2    Davidson, F.A.3
  • 18
    • 0002702117 scopus 로고
    • Nicholson's blowflies revisited
    • 10.1038/287017a0
    • W.S.C. Gurney S.P. Blythe R.M. Nisbet 1990 Nicholson's blowflies revisited Nature 287 17 21 10.1038/287017a0
    • (1990) Nature , vol.287 , pp. 17-21
    • Gurney, W.S.C.1    Blythe, S.P.2    Nisbet, R.M.3
  • 19
    • 0141611851 scopus 로고    scopus 로고
    • Existence of traveling wave solutions in a diffusive predator-prey model
    • 1018.92026 10.1007/s00285-002-0171-9 1963069
    • J. Huang G. Lu S. Ruan 2003 Existence of traveling wave solutions in a diffusive predator-prey model J. Math. Biol. 46 132 152 1018.92026 10.1007/s00285-002-0171-9 1963069
    • (2003) J. Math. Biol. , vol.46 , pp. 132-152
    • Huang, J.1    Lu, G.2    Ruan, S.3
  • 20
    • 33645084765 scopus 로고
    • Circular cause systems in ecology
    • 10.1111/j.1749-6632.1948.tb39854.x
    • G.E. Hutchinson 1948 Circular cause systems in ecology Ann. N. Y. Acad. Sci. 50 221 246 10.1111/j.1749-6632.1948.tb39854.x
    • (1948) Ann. N. Y. Acad. Sci. , vol.50 , pp. 221-246
    • Hutchinson, G.E.1
  • 21
    • 0041313947 scopus 로고    scopus 로고
    • Population growth in space and time: Spatial logistic equations
    • 10.1890/0012-9658(2003)084[0252:PGISAT]2.0.CO;2
    • R. Law D.J. Murrell U. Dieckmann 2003 Population growth in space and time: Spatial logistic equations Ecology 84 252 262 10.1890/0012-9658(2003) 084[0252:PGISAT]2.0.CO;2
    • (2003) Ecology , vol.84 , pp. 252-262
    • Law, R.1    Murrell, D.J.2    Dieckmann, U.3
  • 22
    • 33846155883 scopus 로고    scopus 로고
    • Existence and global attractivity of positive periodic solutions for the impulsive delay Nicholson's blowflies model
    • 1117.34065 10.1016/j.cam.2006.02.001 2293538
    • W.T. Li Y.H. Fan 2007 Existence and global attractivity of positive periodic solutions for the impulsive delay Nicholson's blowflies model J. Comput. Appl. Math. 201 55 68 1117.34065 10.1016/j.cam.2006.02.001 2293538
    • (2007) J. Comput. Appl. Math. , vol.201 , pp. 55-68
    • Li, W.T.1    Fan, Y.H.2
  • 23
    • 84867929521 scopus 로고    scopus 로고
    • Travelling waves and numerical approximations in a reaction advection diffusion equation with nonlocal delayed effects
    • 1017.92024 10.1007/s00332-003-0524-6 1982017
    • D. Liang J. Wu 2003 Travelling waves and numerical approximations in a reaction advection diffusion equation with nonlocal delayed effects J. Nonlinear Sci. 13 289 310 1017.92024 10.1007/s00332-003-0524-6 1982017
    • (2003) J. Nonlinear Sci. , vol.13 , pp. 289-310
    • Liang, D.1    Wu, J.2
  • 24
    • 0002230873 scopus 로고
    • Models for single populations
    • R.M. May (eds). Blackwell Scientific Oxford
    • May, R.M.: Models for single populations. In: May, R.M. (ed.) Theoretical Ecology: Principles and Applications, pp. 4-25. Blackwell Scientific, Oxford (1976)
    • (1976) Theoretical Ecology: Principles and Applications , pp. 4-25
    • May, R.M.1
  • 25
    • 84970543436 scopus 로고
    • Compensatory reactions of populations to stresses, and their evolutionary significance
    • 10.1071/ZO9540001
    • A.J. Nicholson 1954 Compensatory reactions of populations to stresses, and their evolutionary significance Aust. J. Zool. 2 1 8 10.1071/ZO9540001
    • (1954) Aust. J. Zool. , vol.2 , pp. 1-8
    • Nicholson, A.J.1
  • 26
    • 84970556051 scopus 로고
    • An outline of the dynamics of animal populations
    • 10.1071/ZO9540009
    • A.J. Nicholson 1954 An outline of the dynamics of animal populations Aust. J. Zool. 2 9 65 10.1071/ZO9540009
    • (1954) Aust. J. Zool. , vol.2 , pp. 9-65
    • Nicholson, A.J.1
  • 28
    • 0032155119 scopus 로고    scopus 로고
    • Turing instability and traveling waves in diffusive plankton models with delayed nutrient recycling
    • 0911.92028 10.1093/imamat/61.1.15 1656262
    • S. Ruan 1998 Turing instability and traveling waves in diffusive plankton models with delayed nutrient recycling IMA J. Appl. Math. 61 15 32 0911.92028 10.1093/imamat/61.1.15 1656262
    • (1998) IMA J. Appl. Math. , vol.61 , pp. 15-32
    • Ruan, S.1
  • 29
    • 34248517099 scopus 로고    scopus 로고
    • Delay differential equations in single species dynamics
    • O. Arino (eds) et al. Springer New York. 10.1007/1-4020-3647-7-11
    • Ruan, S.: Delay differential equations in single species dynamics. In: Arino, O. et al.(eds.) Delay Differential Equations and Applications, pp. 477-517. Springer, New York (2006)
    • (2006) Delay Differential Equations and Applications , pp. 477-517
    • Ruan, S.1
  • 30
    • 10044257560 scopus 로고    scopus 로고
    • Stability of steady states and existence of traveling waves in a vector disease model
    • 1065.35059 10.1017/S0308210500003590 2099575
    • S. Ruan D. Xiao 2004 Stability of steady states and existence of traveling waves in a vector disease model Proc. R. Soc. Edinburgh Sect. A 134 991 1011 1065.35059 10.1017/S0308210500003590 2099575
    • (2004) Proc. R. Soc. Edinburgh Sect. A , vol.134 , pp. 991-1011
    • Ruan, S.1    Xiao, D.2
  • 31
    • 0001219328 scopus 로고    scopus 로고
    • Dirichlet problem for the diffusive Nicholson's blowflies equation
    • 0923.35195 10.1006/jdeq.1998.3489 1658605
    • J.W.-H. So Y. Yang 1998 Dirichlet problem for the diffusive Nicholson's blowflies equation J. Diff. Equ. 150 317 348 0923.35195 10.1006/jdeq.1998.3489 1658605
    • (1998) J. Diff. Equ. , vol.150 , pp. 317-348
    • So, J.W.-H.1    Yang, Y.2
  • 32
    • 0035882630 scopus 로고    scopus 로고
    • Travelling waves for the diffusive Nicholson's blowflies equation
    • 1027.35051 10.1016/S0096-3003(00)00055-2 1842616
    • J.W.-H. So X. Zou 2001 Travelling waves for the diffusive Nicholson's blowflies equation Appl. Math. Comput. 122 385 392 1027.35051 10.1016/S0096-3003(00)00055-2 1842616
    • (2001) Appl. Math. Comput. , vol.122 , pp. 385-392
    • So, J.W.-H.1    Zou, X.2
  • 33
    • 0347948008 scopus 로고    scopus 로고
    • Numerical Hopf bifurcation analysis on the diffusive Nicholson's blowflies equation
    • 10.1016/S0096-3003(99)00047-8 1745907
    • J.W.-H. So J. Wu Y. Yang 2000 Numerical Hopf bifurcation analysis on the diffusive Nicholson's blowflies equation Appl. Math. Comput. 111 53 69 10.1016/S0096-3003(99)00047-8 1745907
    • (2000) Appl. Math. Comput. , vol.111 , pp. 53-69
    • So, J.W.-H.1    Wu, J.2    Yang, Y.3
  • 34
    • 32044440101 scopus 로고    scopus 로고
    • A reaction-diffusion model for a single species with age structure. I. Travelling wavefronts on unbounded domains
    • 1852431
    • J.W.-H. So J. Wu X. Zou 2003 A reaction-diffusion model for a single species with age structure. I. Travelling wavefronts on unbounded domains Proc. R. Soc. Lond. Ser. A 457A 1841 1853 1852431
    • (2003) Proc. R. Soc. Lond. Ser. A , vol.457 , pp. 1841-1853
    • So, J.W.-H.1    Wu, J.2    Zou, X.3
  • 35
    • 32044459052 scopus 로고    scopus 로고
    • Travelling wave-fronts in reaction-diffusion systems with spatio-temporal delays
    • 1100.35050 10.1016/j.jde.2005.08.010 2200751
    • Z.C. Wang W.T. Li S. Ruan 2006 Travelling wave-fronts in reaction-diffusion systems with spatio-temporal delays J. Differ. Equ. 222 185 232 1100.35050 10.1016/j.jde.2005.08.010 2200751
    • (2006) J. Differ. Equ. , vol.222 , pp. 185-232
    • Wang, Z.C.1    Li, W.T.2    Ruan, S.3
  • 36
    • 12244312783 scopus 로고    scopus 로고
    • Hopf bifurcation analysis in a delayed Nicholson's blowflies equation
    • 1144.34373 10.1016/j.na.2003.04.002 2112957
    • J. Wei M.Y. Li 2005 Hopf bifurcation analysis in a delayed Nicholson's blowflies equation Nonlinear Anal. TMA 60 1351 1367 1144.34373 10.1016/j.na.2003.04.002 2112957
    • (2005) Nonlinear Anal. TMA , vol.60 , pp. 1351-1367
    • Wei, J.1    Li, M.Y.2
  • 37
    • 0343717093 scopus 로고    scopus 로고
    • Travelling wave-fronts of reaction-diffusion systems with delay
    • 0996.34053 10.1023/A:1016690424892 1845097
    • J. Wu X. Zou 2001 Travelling wave-fronts of reaction-diffusion systems with delay J. Dyn. Differ. Equ. 13 651 687 0996.34053 10.1023/A:1016690424892 1845097
    • (2001) J. Dyn. Differ. Equ. , vol.13 , pp. 651-687
    • Wu, J.1    Zou, X.2
  • 38
    • 3242726256 scopus 로고    scopus 로고
    • Dynamics for the diffusive Nicholson's blowflies equation
    • W. Chen S. Hu (eds). Southwest Missouri State University Springfield
    • Yang, Y., So, J.W.-H.: Dynamics for the diffusive Nicholson's blowflies equation. In: Chen, W., Hu, S. (eds.) Dynamical Systems and Differential Equations. vol. 11, pp. 333-352. Southwest Missouri State University, Springfield (1998)
    • (1998) Dynamical Systems and Differential Equations , vol.11 , pp. 333-352
    • Yang, Y.1    So, J.W.-H.2
  • 39
    • 0037106115 scopus 로고    scopus 로고
    • Delay induced traveling wave-fronts in reaction diffusion equations of KPP-Fisher type
    • 1058.35114 10.1016/S0377-0427(02)00363-1 1925963
    • X. Zou 2002 Delay induced traveling wave-fronts in reaction diffusion equations of KPP-Fisher type J. Comput. Appl. Math. 146 309 321 1058.35114 10.1016/S0377-0427(02)00363-1 1925963
    • (2002) J. Comput. Appl. Math. , vol.146 , pp. 309-321
    • Zou, X.1


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