Global analysis of a stage-structured model with population diffusion

References

• Iannelli , M . 1995 . “ Mathematical Theory of Age-structured Population Dynamics ” . In Applied Mathematics Monograph C.N.R , Vol. 7 , Pisa : Giardini Editori e Stampatori .
   Google Scholar
• Webb , G . 1985 . Theory of Nonlinear Age-dependent Population Dynamics , Vol. 89 , New York : Marcel Dekker .
   Google Scholar
• Aiello , WG and Freedman , HI . 1990 . A time delay model of single-species growth with stage structure . Math. Biosci. , 101 : 139 – 153 .
   PubMed Web of Science ®Google Scholar
• Aiello , WG , Freedman , HI and Wu , J . 1992 . Analysis of a model representing stage-structured population growth with state-dependent time delay . SIAM J. Appl. Math. , 52 : 855 – 869 .
   Web of Science ®Google Scholar
• Gourley , SA and Kuang , Y . 2004 . A stage structured predator–prey model and its dependence on maturation delay and death rate . J. Math. Biol. , 49 : 188 – 200 .
   PubMed Web of Science ®Google Scholar
• Liu , S and Beretta , E . 2006 . A stage-structured predator–prey model of Beddington–DeAngelis type . SIAM J. Appl. Math. , 66 : 1101 – 1129 .
   Google Scholar
• Liu , S , Chen , L and Agarwal , R . 2002 . Recent progress on stage-structured population dynamics . Math. Comput. Model. , 36 : 1319 – 1360 .
   Google Scholar
• Thieme , H . 2003 . Mathematics in Population Biology , Princeton, NJ : Princeton University Press .
   Google Scholar
• Wang , W , Mulone , G , Salemi , F and Salone , V . 2001 . Permanence and stability of a stage-structured predator–prey model . J. Math. Anal. Appl. , 262 : 499 – 528 .
   Google Scholar
• Wang , W . 2006 . “ Stability of structured prey–predator model ” . In Proceedings of WASCOM 2005 , Edited by: Monaco , R , Mulone , G , Rionero , S and Ruggeri , T . 542 – 547 . River Edge, NJ : Word Scientific .
   Google Scholar
• Wang , W and Chen , L . 1997 . A predator–prey system with stage-structure for predator . Comput. Math. Appl. , 33 : 83 – 91 .
   Web of Science ®Google Scholar
• Wang , W , Takeuchi , Y , Saito , Y and Nakaoka , S . 2006 . Prey–predator system with parental care for predators . J. Theoretical Biol. , 241 : 451 – 458 .
   PubMedGoogle Scholar
• Henry , D . 1981 . “ Geometric Theory of Semilinear Parabolic Equations ” . In Lecture Notes in Mathematics , Vol. 840 , Berlin, New York : Springer .
   Google Scholar
• Pang , PYH and Wang , M . 2004 . Strategy and stationary pattern in a three-species predator-prey model . J. Differ. Eqns , 200 : 245 – 273 .
   Web of Science ®Google Scholar
• O.A. Ladyženskaja, V.A. Solonnikov and N.N. Ural'ceva, Linear and Quasilinear Equations of parabolic type. (Russian) (Translated from the Russian by S. Smith.), Translations of Mathematical Monographs, Vol. 23, American Mathematical Society, Providence, RI, 1967.
   Google Scholar
• Friedman , A . 1976 . Partial Differential Equations , New York : Krieger .
   Google Scholar
• Wang , W and Zhao , X . 2004 . An epidemic model in a patchy environment . Math. Biosci. , 190 : 97 – 112 .
   PubMed Web of Science ®Google Scholar
• Pao , CV . 1992 . Nonlinear Parabolic and Elliptic Equations , New York : Plenum Press .
   Google Scholar
• Hale , JK and Waltman , P . 1989 . Persistence in infinite-dimensional systems . SIAM J. Math. Anal. , 20 : 388 – 395 .
   Web of Science ®Google Scholar
• Zhao , X . 2003 . Dynamical Systems in Population Biology , New York : Springer .
   Google Scholar
• J. Smoller, Shock Waves and Reaction–diffusion Equations, Grundlehren der Mathematischen Wissenschaften, 2nd ed., Vol. 258, Springer-Verlag, New York, 1994.
   Google Scholar
• Ladyženskaja , OA and Solonnikov , VA . 1973 . The linearization principle and invariant manifolds for problems of magnetohydrodynamics. (Russian) Boundary value problems of mathematical physics and related questions in the theory of functions . Zap. Naucn. Sem. Leningrad. Otdel. Mat. Inst. Steklov. (LOMI) , 38 : 46 – 93 .
   Google Scholar
• G. Mulone, Nonlinear stability for reaction–diffusion models, in First International Conference on new trends in fluid and solid models, Proceedings of the International Conference in Honour of Brian Straughan, Vietri sul Mare (SA), Italy, 28 February–1 March 2008, World Scientific, Hackensack, NJ, 2009, pp. 91–102.
   Google Scholar
• Mulone , G and Solonnikov , VA . 2009 . Linearization principle for a system of equations of mixed type . Nonlinear Anal. , 71 : 1019 – 1031 .
   Web of Science ®Google Scholar