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Global dynamics of a predator-prey system with density-dependent mortality and ratio-dependent functional response
The spatial dynamics of a Zebra mussel model in river environments
1. | Department of Mathematics, University of Nebraska-Lincoln, Lincoln, NE 68588, USA |
2. | Department of Mathematics and Statistics, Memorial University of Newfoundland, St. John's, NL A1C5S7, Canada |
Huang et al. [
References:
[1] |
D. T. E. Bastviken, N. F. Caraco and J. J. Cole,
Experimental measurements of zebra mussel (Dreissena polymorpha) impacts on phytoplankton community composition, Freshwater Biology, 39 (1998), 375-386.
doi: 10.1046/j.1365-2427.1998.00283.x. |
[2] |
E. Brian Davies, Linear Operators and their Spectra,, Cambridge University Press, 2007.
doi: 10.1017/CBO9780511618864.![]() ![]() |
[3] |
H. Caswell, Matrix Population Models, Sinauer Associates Inc, 2nd edition, 2000. Google Scholar |
[4] |
K. Deimling, Nonlinear Functional Analysis, , Springer-Verlag, Berlin, Heidelberg, 1985.
doi: 10.1007/978-3-662-00547-7. |
[5] |
Y. Du, Order Structure and Topological Methods in Nonlinear Partial Differential Equations: Maximum Principles and Applications, , Volume 1 (Partial Differential Equations and Application), World Scientific Pub Co Inc, 2006.
doi: 10.1142/9789812774446. |
[6] |
J. Fang and X.-Q. Zhao,
Traveling waves for monotone semiflows with weak compactness, SIAM Journal on Mathematical Analysis, 46 (2014), 3678-3704.
doi: 10.1137/140953939. |
[7] |
D. W. Garton and W. R. Haag, Seasonal reproductive cycles and settlement patterns of Dreissena polymorpha in western Lake Erie, in Zebra Mussels: Biology, Impacts, and Control, T. F. Nalepa and D. W. Schloesser, eds., Lewis Publishers, Boca Raton, FL, 1993, 111-128. Google Scholar |
[8] |
P. Hess, Periodic-Parabolic Boundary Value Problems and Positivity, Pitman Search Notes in Mathematics Series, Vol.247, Longman Scientific Technical, Harlow, UK, 1991. |
[9] |
S.-B. Hsu and X.-Q. Zhao,
Spreading speeds and traveling waves for non-monotone integro-difference equations, SIAM Journal on Mathematical Analysis, 40 (2008), 776-789.
doi: 10.1137/070703016. |
[10] |
Q. Huang, H. Wang and M. A. Lewis,
A hybrid continudous/discrete-time model for invasion dynamics of zebra mussles in rivers, SIAM Journal on Applied Mathematics, 77 (2017), 854-880.
doi: 10.1137/16M1057826. |
[11] |
X. Liang, Y. Yi and X.-Q. Zhao,
Spreading speeds and traveling waves for periodic evolution systems, Journal of Differential Equations, 231 (2006), 57-77.
doi: 10.1016/j.jde.2006.04.010. |
[12] |
X. Liang and X.-Q. Zhao,
Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Comm. Pure Appl. Math., 61 (2008), 137-138.
doi: 10.1002/cpa.20221. |
[13] |
X. Liang, L. Zhang and X.-Q. Zhao,
The principal eigenvalue for degenerate periodic reaction-diffusion systems, SIAM Journal on Mathematical Analysis, 49 (2017), 3603-3636.
doi: 10.1137/16M1108832. |
[14] |
P. Magal and X.-Q. Zhao,
Global attractors and steady states for uniformly persistent dynamical systems, SIAM Journal on Mathematical Analysis, 37 (2005), 251-275.
doi: 10.1137/S0036141003439173. |
[15] |
H. W. Mckenzie, Y. Jin, J. Jacobsen and M. A. Lewis,
$R_0$ analysis of a spatiotemporal model for a stream population, SIAM Journal on Applied Dynamical Systems, 11 (2012), 567-596.
doi: 10.1137/100802189. |
[16] |
M. G. Neubert and H. Caswell, Demography and dispersal: Calculation and sensitivity analysis of invasion speed for structured populations, Ecology, 81 (2000), 1613-1628. Google Scholar |
[17] |
A. Ricciardi, F. G. Whoriskey and J. B. Rasmussen,
Impact of the Dreissena invasion on native unionid bivalves in the upper St. Lawrence River, The Canadian Journal of Fisheries and Aquatic Sciences, 53 (1996), 1434-1444.
doi: 10.1139/f96-068. |
[18] |
H. L. Smith and X.-Q. Zhao,
Robust persistence for semidynamical systems, Nonlinear Analysis, 47 (2001), 6169-6179.
doi: 10.1016/S0362-546X(01)00678-2. |
[19] |
H. R. Thieme,
Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity, SIAM Journal on Applied Mathematics, 70 (2009), 188-211.
doi: 10.1137/080732870. |
[20] |
X. Wang and X.-Q. Zhao,
Target reproduction numbers for reaction-diffusion population models, Journal of Mathematical Biology, 81 (2020), 625-647.
doi: 10.1007/s00285-020-01523-9. |
[21] |
H. F. Weinberger,
Long-time behavior of a class of biological models, SIAM Journal on Mathematical Analysis, 13 (1982), 353-396.
doi: 10.1137/0513028. |
[22] |
H. F. Weinberger,
On spreading speeds and traveling waves for growth and migration models in a periodic habitat, Journal of Mathematical Biology, 45 (2002), 511-548.
doi: 10.1007/s00285-002-0169-3. |
[23] |
H. F. Weinberger, K. Kawasaki and N. Shigesada,
Spreading speeds of spatially periodic integro-difference models for populations with non-monotone recruitment functions, Journal of Mathematical Biology, 57 (2008), 387-411.
doi: 10.1007/s00285-008-0168-0. |
[24] |
P. Weng and X.-Q. Zhao,
Spreading speed and traveling waves for a multi-type SIS epidemic model, Journal of Differential Equations, 229 (2006), 270-296.
doi: 10.1016/j.jde.2006.01.020. |
[25] |
R. Wu and X.-Q. Zhao,
Spatial invasion of a birth pulse populatoin with nonlocal dispersal, SIAM Journal on Applied Mathematics, 79 (2019), 1075-1097.
doi: 10.1137/18M1209805. |
[26] |
X.-Q. Zhao, Dynamical Systems in Population Biology, , second edition, Springer, New York, 2017.
doi: 10.1007/978-3-319-56433-3. |
show all references
References:
[1] |
D. T. E. Bastviken, N. F. Caraco and J. J. Cole,
Experimental measurements of zebra mussel (Dreissena polymorpha) impacts on phytoplankton community composition, Freshwater Biology, 39 (1998), 375-386.
doi: 10.1046/j.1365-2427.1998.00283.x. |
[2] |
E. Brian Davies, Linear Operators and their Spectra,, Cambridge University Press, 2007.
doi: 10.1017/CBO9780511618864.![]() ![]() |
[3] |
H. Caswell, Matrix Population Models, Sinauer Associates Inc, 2nd edition, 2000. Google Scholar |
[4] |
K. Deimling, Nonlinear Functional Analysis, , Springer-Verlag, Berlin, Heidelberg, 1985.
doi: 10.1007/978-3-662-00547-7. |
[5] |
Y. Du, Order Structure and Topological Methods in Nonlinear Partial Differential Equations: Maximum Principles and Applications, , Volume 1 (Partial Differential Equations and Application), World Scientific Pub Co Inc, 2006.
doi: 10.1142/9789812774446. |
[6] |
J. Fang and X.-Q. Zhao,
Traveling waves for monotone semiflows with weak compactness, SIAM Journal on Mathematical Analysis, 46 (2014), 3678-3704.
doi: 10.1137/140953939. |
[7] |
D. W. Garton and W. R. Haag, Seasonal reproductive cycles and settlement patterns of Dreissena polymorpha in western Lake Erie, in Zebra Mussels: Biology, Impacts, and Control, T. F. Nalepa and D. W. Schloesser, eds., Lewis Publishers, Boca Raton, FL, 1993, 111-128. Google Scholar |
[8] |
P. Hess, Periodic-Parabolic Boundary Value Problems and Positivity, Pitman Search Notes in Mathematics Series, Vol.247, Longman Scientific Technical, Harlow, UK, 1991. |
[9] |
S.-B. Hsu and X.-Q. Zhao,
Spreading speeds and traveling waves for non-monotone integro-difference equations, SIAM Journal on Mathematical Analysis, 40 (2008), 776-789.
doi: 10.1137/070703016. |
[10] |
Q. Huang, H. Wang and M. A. Lewis,
A hybrid continudous/discrete-time model for invasion dynamics of zebra mussles in rivers, SIAM Journal on Applied Mathematics, 77 (2017), 854-880.
doi: 10.1137/16M1057826. |
[11] |
X. Liang, Y. Yi and X.-Q. Zhao,
Spreading speeds and traveling waves for periodic evolution systems, Journal of Differential Equations, 231 (2006), 57-77.
doi: 10.1016/j.jde.2006.04.010. |
[12] |
X. Liang and X.-Q. Zhao,
Asymptotic speeds of spread and traveling waves for monotone semiflows with applications, Comm. Pure Appl. Math., 61 (2008), 137-138.
doi: 10.1002/cpa.20221. |
[13] |
X. Liang, L. Zhang and X.-Q. Zhao,
The principal eigenvalue for degenerate periodic reaction-diffusion systems, SIAM Journal on Mathematical Analysis, 49 (2017), 3603-3636.
doi: 10.1137/16M1108832. |
[14] |
P. Magal and X.-Q. Zhao,
Global attractors and steady states for uniformly persistent dynamical systems, SIAM Journal on Mathematical Analysis, 37 (2005), 251-275.
doi: 10.1137/S0036141003439173. |
[15] |
H. W. Mckenzie, Y. Jin, J. Jacobsen and M. A. Lewis,
$R_0$ analysis of a spatiotemporal model for a stream population, SIAM Journal on Applied Dynamical Systems, 11 (2012), 567-596.
doi: 10.1137/100802189. |
[16] |
M. G. Neubert and H. Caswell, Demography and dispersal: Calculation and sensitivity analysis of invasion speed for structured populations, Ecology, 81 (2000), 1613-1628. Google Scholar |
[17] |
A. Ricciardi, F. G. Whoriskey and J. B. Rasmussen,
Impact of the Dreissena invasion on native unionid bivalves in the upper St. Lawrence River, The Canadian Journal of Fisheries and Aquatic Sciences, 53 (1996), 1434-1444.
doi: 10.1139/f96-068. |
[18] |
H. L. Smith and X.-Q. Zhao,
Robust persistence for semidynamical systems, Nonlinear Analysis, 47 (2001), 6169-6179.
doi: 10.1016/S0362-546X(01)00678-2. |
[19] |
H. R. Thieme,
Spectral bound and reproduction number for infinite-dimensional population structure and time heterogeneity, SIAM Journal on Applied Mathematics, 70 (2009), 188-211.
doi: 10.1137/080732870. |
[20] |
X. Wang and X.-Q. Zhao,
Target reproduction numbers for reaction-diffusion population models, Journal of Mathematical Biology, 81 (2020), 625-647.
doi: 10.1007/s00285-020-01523-9. |
[21] |
H. F. Weinberger,
Long-time behavior of a class of biological models, SIAM Journal on Mathematical Analysis, 13 (1982), 353-396.
doi: 10.1137/0513028. |
[22] |
H. F. Weinberger,
On spreading speeds and traveling waves for growth and migration models in a periodic habitat, Journal of Mathematical Biology, 45 (2002), 511-548.
doi: 10.1007/s00285-002-0169-3. |
[23] |
H. F. Weinberger, K. Kawasaki and N. Shigesada,
Spreading speeds of spatially periodic integro-difference models for populations with non-monotone recruitment functions, Journal of Mathematical Biology, 57 (2008), 387-411.
doi: 10.1007/s00285-008-0168-0. |
[24] |
P. Weng and X.-Q. Zhao,
Spreading speed and traveling waves for a multi-type SIS epidemic model, Journal of Differential Equations, 229 (2006), 270-296.
doi: 10.1016/j.jde.2006.01.020. |
[25] |
R. Wu and X.-Q. Zhao,
Spatial invasion of a birth pulse populatoin with nonlocal dispersal, SIAM Journal on Applied Mathematics, 79 (2019), 1075-1097.
doi: 10.1137/18M1209805. |
[26] |
X.-Q. Zhao, Dynamical Systems in Population Biology, , second edition, Springer, New York, 2017.
doi: 10.1007/978-3-319-56433-3. |
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