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Mathematical Biosciences and Engineering (MBE)
 

Bifurcation analysis and transient spatio-temporal dynamics for a diffusive plant-herbivore system with Dirichlet boundary conditions
Pages: 699 - 715, Issue 4, August 2015

doi:10.3934/mbe.2015.12.699      Abstract        References        Full text (2913.5K)                  Related Articles

Lin Wang - Department of Mathematics and Statistics, University of New Brunswick, Fredericton, NB, E3B 5A3, Canada (email)
James Watmough - Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3, Canada (email)
Fang Yu - Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3, Canada (email)

1 J. Blat and K. J. Brown, Global bifurcation of positive solutions in some system of elliptic equations, SIAM J. Math. Anal., 17 (1986), 1339-1353.       
2 E. Conway, R. Gardner and J. Smoller, Stability and bifurcation of steady-state solutions for predator-prey equations, Adv. in Appl. Math., 3 (1982), 288-334.       
3 M. G. Crandall and P. H. Rabinowitz, Bifurcation from simple eigenvalues, J. Funct. Anal., 8 (1971), 321-340.       
4 E. N. Dancer, On positive solutions of some pairs of differential equations, Trans. Amer. Math. Soc., 284 (1984), 729-743.       
5 E. N. Dancer, On positive solutions of some pairs of differential equations II, J. Diff. Equat., 60 (1985), 236-258.       
6 L. R. Fox, Defense and dynamics in plant-herbivore systems, Amer. Zool., 21 (1981), 853-864.
7 B. D. Hassard, N. D. KazavinoJ and Y. H. Wan, Theory and Applications of the Hopf Bifurcation, Cambridge University Press, Cambridge, MA, 1981.       
8 L. R. Ginzburg, Assuming reproduction to be a function of consumption raises doubts about some popular predator-prey models, J. of Animal Ecology, 67 (1998), 325-327.
9 L. Li, Coexistence theorems of steady states for predator-prey interacting systems, Trans. Amer. Math. Soc., 305 (1988), 143-166.       
10 R. E. Ricklefs, The Economy of Nature, Freeman and Company, New York, 2010.
11 Y. Su and X. Zou, Transient oscillatory patterns in the diffusive non-local blowfly equation with delay under the zero-flux boundary condition, Nonlinearity, 27 (2014), 87-104.
12 Y. Yamada, Stability of steady states for prey-predator diffusion equations with homogeneous Dirichlet conditions, SIAM J. Math. Anal., 21 (1990), 327-345.       

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