Wavefronts of a stage structured model with statedependent delay
Pages: 4931  4954,
Issue 10,
October
2015
doi:10.3934/dcds.2015.35.4931 Abstract
References
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Yunfei Lv  Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China (email)
Rong Yuan  School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China (email)
Yuan He  School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, China (email)
1 
M. Adimy, F. Crauste, M. Hbid and R. Qesmi, Stability and Hopf bifurcation for a cell population model with statedependent delay, SIAM J. Appl. Math., 70 (2010), 16111633. 

2 
W. Aiello and H. Freedman, A timedelay model of a single species growth with stage structure, Math. Biosci, 101 (1990), 139153. 

3 
W. Aiello, H. Freedman and J. Wu, Analysis of a model representing stagestructured population growth with statedependent time delay, SIAM J. Appl. Math, 52 (1992), 855869. 

4 
J. Alomari and S. Gourley, Stability and traveling fronts in LotkaVolterra competition models with stage structure, SIAM J. Appl. Math., 63 (2003), 20632086. 

5 
J. AlOmari and S. Gourley, Dynamics of a stagestructured population model incorporating a statedependent maturation delay, Nonlinear Anal. Real World Appl., 6 (2005), 1333. 

6 
J. AlOmari and A. Tallafha, Modelling and analysis of stagestructured population model with statedependent maturation delay and harvesting, Int. J. Math. Analysis, 1 (2007), 391407. 

7 
H. Andrewartha and L. Birch, The Distribution and Abundance of Animals, University of Chicago Press, Chicago, IL, 1954, p. 370. 

8 
H. Barclay and P. driessche, A model for a single species with two life history stages and added mortality, Ecol. Model, 11 (1980), 157166. 

9 
M. Benchohra, I. Medjadj, J. Nieto and P. Prakash, Global existence for functional differential equations with statedependent delay, J. Funct. Space Appl., (2013), Art. ID 863561, 7 pp. 

10 
J. Canosa, On a nonlinear diffusion equation describing population growth, IBM J. Res. Develop., 17 (1973), 307313. 

11 
K. Das and S. Ray, Effect of delay on nutrient cycling in phytoplanktonzooplankton interactions in estuarine system, Ecol. Model., 215 (2008), 6976. 

12 
R. Gambell, Birds and mammalsAntarctic whales, in Antarctica (eds. W. Bonner and D. Walton), Pergamon Press, New York, 1985, 223241. 

13 
S. Gourley and Y. Kuang, Wavefronts and global stability in a timedelayed population model with stage structure, Proc. R. Soc. Lond. A, 459 (2003), 15631579. 

14 
W. Gurney, R. Nisbet and J. Lawton, The systematic formulation of tractible single species population models incorporating age structure, J. Animal Ecol., 52 (1983), 479485. 

15 
J. Hale, Theory of Functional Differential Equations, SpringerVerlag, New York, 1977. 

16 
F. Hartung, T. Krisztin, H. Walther and J. Wu, Functional differential equations with statedependent delay: Theory and applications, in Handbook of Differential Equations: Ordinary Differential Equations. Vol. III (eds. A. Canada, P. Drabek and A. Fonda), Elsevier Science B. V., NorthHolland, Amsterdam, 2006, 435545. 

17 
K. Hong and P. Weng, Stability and traveling waves of a stagestructured predatorprey model with Holling typeII functional response and harvesting, Nonlinear Anal. Real World Appl., 14 (2013), 83103. 

18 
Q. Hu and X. Zhao, Global dynamics of a statedependent delay model with unimodal feedback, J. Math. Anal. Appl., 399 (2013), 133146. 

19 
D. Jones and C. Walters, Catastrophe theory and fisheries regulation, J. Fish. Res. Bd. Can., 33 (1976), 28292833. 

20 
T. Krisztin, A local unstable manifold for differential equations with statedependent delay, Discret. Contin. Dyn. S., 9 (2003), 9931028. 

21 
T. Krisztin and A. Rezounenko, Parabolic partial differential equations with discrete statedependent delay: Classical solutions and solution manifold, preprint, November 30, 2014, arXiv:1412.0219. 

22 
Y. Kuang, Delay Differential Equation with Applications in Population Dynamics, Academic, New York, 1993. 

23 
H. Landahl and B. Hanson, A three stage population model with cannibalism, Bull. Math. Biol., 37 (1975), 1117. 

24 
X. Liang and X. Zhao, Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Comm. Pure Appl. Math., 60 (2007), 140; Comm. Pure Appl. Math., 61 (2008), 137138 (erratum). 

25 
M. Memory, Stable and unstable manifolds for partial functional differential equations, Nonlinear Anal., 16 (1991), 131142. 

26 
J. Murray, Mathematical Biology, Springer, 1989. 

27 
A. Rezounenko and J. Wu, A nonlocal PDE model for population dynamics with stateselective delay: Local theory and global attractors, J. Comput. Appl. Math., 190 (2006), 99113. 

28 
W. Rudin, Functional Analysis, McGrawHill, 1991. 

29 
K. Schaaf, Asymptotic behavior and travelling wave solutions for parabolic functional differential equations, Trans. Amer. Math. Soc., 302 (1987), 587615. 

30 
J. Sherratt, Wavefront propagation in a competition equation with a new motility term modelling contact inhibition between cell populations, Proc. R. Soc. Lond. A, 456 (2000), 23652386. 

31 
K. Tognetti, The two stage stochastic model, Math. Biosci., 25 (1975), 195204. 

32 
C. Travis and G. Webb, Existence and stability for partial functional differential equations, Trans. Amer. Math. Soc., 200 (1974), 395418. 

33 
H. Wang, On the existence of traveling waves for delayed reactiondiffusion equations, J. Differential Equations, 247 (2009), 887905. 

34 
S. Wood, S. Blythe, W. Gurney and R. Nisbet, Instability in mortality estimation schemes related to stagestructure population models, IMA J. Math. Appl. in Medicine and Biology, 6 (1989), 4768. 

35 
J. Wu, Theory and Applications of Partial Functional Differential Equations, SpringerVerlag, New York, 1996. 

36 
Y. Yang, Hopf bifurcation in a twocompetitor, oneprey system with time delay, Appl. Math. Comput., 214 (2009), 228235. 

37 
Q. Ye, Z. Li, M. Wang and Y. Wu, Introduction of ReactionDiffusion Equations, Second edition, China Science Publishing Group, 2011. 

38 
A. Zaghrout and S. Attalah, Analysis of a model of stagestructured population dynamics growth with time statedependent time delay, Appl. Math. Comput., 77 (1996), 185194. 

39 
G. Zhang, W. Li and G. Lin, Traveling waves in delayed predatorprey systems with nonlocal diffusion and stage structure, Math. Comput. Model., 49 (2009), 10211029. 

40 
L. Zhang, B. Li and J. Shang, Stability and travelling waves for a timedelayed population system with stage structure, Nonlinear Anal. Real World Appl., 13 (2012), 14291440. 

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