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Original Articles

Bifurcation analysis in a diffusive ‘food-limited’ model with time delay

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Pages 1161-1181 | Received 19 Mar 2009, Accepted 22 May 2009, Published online: 20 Nov 2009

References

  • Smith , FE . 1963 . Population dynamics in Daphnia magna . Ecology , 44 : 651 – 663 .
  • Gopalsamy , K , Kulenovic , MRS and Ladas , G . 1988 . Time lags in a ‘food-limited’ population model . Appl. Anal. , 31 : 225 – 237 .
  • Gopalsamy , K , Kulenovic , MRS and Ladas , G . 1990 . Environmental periodicity and time delays in ‘food-limited’ population model . J. Math. Anal. Appl. , 147 : 545 – 555 .
  • Wan , A and Wei , J . 2009 . Hopf bifurcation analysis of a food-limited population model with delay . Nonlinear Anal. Real World Appl. , DOI:10.1016/j.nonrwa.2009.01.052
  • Wu , J . 1996 . Theory and Applications of Partial Functional-differential Equations , New York : Springer .
  • Berezansky , L and Braverman , K . 2003 . On oscillation of a food-limited population model with time delay . Abstr. Appl. Anal. , 2003 ( 1 ) : 55 – 56 .
  • Chen , FD , Sun , DX and Shi , JL . 2003 . Periodicity in a food-limited population model with toxicants and state dependent delays . J. Math. Anal. Appl. , 288 : 136 – 146 .
  • Fan , M and Wang , K . 2002 . Periodicity in a ‘food-limited’ population model with toxicants and time delays . Acta Math. Appl. Sin. (Eng. Ser.) , 18 : 309 – 314 .
  • Grove , EA , Ladas , G and Qian , C . 1993 . Global attractivity in a ‘food-limited’ population model . Dynam. Syst. Appl. , 2 : 243 – 249 .
  • Jiang , D , Shi , N and Zhao , Y . 2005 . Existence, uniqueness, and global stability of positive solution to the food-limited population model with random peturbation . Math. Comput. Model. , 42 : 651 – 658 .
  • So , JW-H and Yu , JS . 1995 . On the uniform stability for a ‘food-limited’ population model with time delay . Proc. Roy. Soc. Edinburgh , 125A : 991 – 1002 .
  • Tang , S and Chen , L . 2004 . Global attractivity in a ‘food-limited’ population model with impulsive effects . J. Math. Anal. Appl. , 292 : 211 – 221 .
  • Davidson , FS and Gourley , SA . 2001 . The effects of temporal delays in a model for a food-limited, diffusing population . J. Math. Anal. Appl. , 261 : 633 – 648 .
  • Su , Y , Wei , J and Shi , JP . 2009 . Hopf bifurcations in a reaction-diffusion population model with delay effect . J. Differ. Equ. , 247 : 1156 – 1184 .
  • Gourley , SA . 2001 . Wave front solution of a diffusive delay model for populations of Daphnia magna . Comp. Math. Appl. , 42 : 1421 – 1430 .
  • Gourley , SA and Chaplain , MAJ . 2002 . Travelling fronts in a food-limited population model with time delay . Proc. Roy. Soc. Edinburgh , 132A : 75 – 89 .
  • Feng , W and Lu , X . 1999 . On diffusive population models with toxicants and time delays . J. Math. Anal. Appl. , 233 : 373 – 386 .
  • Wang , ZC and Li , WT . 2007 . Monotone travelling fronts of a food-limited population model with nonlocal delay . Nonlinear Anal. Real World Appl. , 8 : 699 – 712 .
  • Wang , JL , Zhou , L and Tang , YB . 2006 . Asymptotic periodicity of a food-limited diffusive population model with time-delay . J. Math. Appl. , 313 : 382 – 399 .
  • Robinson , JC . 2001 . Infinite-dimensional Dynamical Systems–An Introduction to Dissipative Parabolic PDEs and Theory of Global Attractors , Cambridge : Cambridge University Press .
  • Lin , X , So , JW-H and Wu , J . 1992 . Centre manifolds for partial differential equations with delays . Proc. Roy. Soc. Edinburgh , 122A : 237 – 254 .
  • Faria , T . 2000 . Normal forms and Hopf bifurcation for partial differential equations with delays . Trans. Am. Math. Soc. , 352 : 2217 – 2238 .
  • Su , Y , Wei , J and Shi , JP . 2009 . Bifurcation analysis in a delayed diffusive Nicholsons blowflies equation . Nonlinear Anal. Real World Appl. , DOI:10.1016/j.nonrwa.2009.03.024
  • Ruan , S and Wei , J . 2003 . On the zeros of transcendental functions with applications to stability of delay differential equations with two delays . Dynam. Contin. Discrete Impuls. Syst. Ser. A Math. Anal. , 10 : 863 – 874 .
  • Faria , T . 1995 . Normal forms for retarded functional differential equations with parameters and applications to Hopf bifurcation . J. Differ. Equ. , 122 : 181 – 200 .

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