The role of protection zone on species spreading governed by a reaction–diffusion model with strong Allee effect

[1]  Rui Peng,et al.  The Fisher-KPP equation over simple graphs: varied persistence states in river networks , 2020, Journal of mathematical biology.

[2]  M. Kot,et al.  Integrodifference Equations , 2019, Encyclopedia of Theoretical Ecology.

[3]  Rui Peng,et al.  Population Dynamics in River Networks , 2019, Journal of Nonlinear Science.

[4]  Yan Wang,et al.  Persistence and extinction of population in reaction–diffusion–advection model with strong Allee effect growth , 2019, Journal of Mathematical Biology.

[5]  Lingyu Liu,et al.  Effect of the protection zone on coexistence of the species for a ratio-dependent predator-prey model , 2018 .

[6]  Yoshio Yamada,et al.  Effect of cross-diffusion in the diffusion prey-predator model with a protection zone II , 2017 .

[7]  Sanyang Liu,et al.  Effect of cross-diffusion on the stationary problem of a Leslie prey-predator model with a protection zone , 2017 .

[8]  A. Shaw,et al.  Density dependence in demography and dispersal generates fluctuating invasion speeds , 2017, Proceedings of the National Academy of Sciences.

[9]  K. Anderson,et al.  Geometric indicators of population persistence in branching continuous-space networks , 2017, Journal of mathematical biology.

[10]  Sining Zheng,et al.  Protection zone in a diffusive predator–prey model with Beddington–DeAngelis functional response , 2015, Journal of mathematical biology.

[11]  Junping Shi,et al.  Effect of harvesting quota and protection zone in a reaction-diffusion model arising from fishery management , 2017 .

[12]  Effect of cross-diffusion in the diffusion prey-predator model with a protection zone , 2016 .

[13]  Nguyen Huu Du,et al.  Protection Zones for Survival of Species in Random Environment , 2016, SIAM J. Appl. Math..

[14]  Yuan Lou,et al.  The Emergence of Range Limits in Advective Environments , 2016, SIAM J. Appl. Math..

[15]  C. B. Muratov,et al.  Threshold phenomena for symmetric-decreasing radial solutions of reaction-diffusion equations , 2015, 1506.09146.

[16]  Protection zone in a modified Lotka-Volterra model , 2015 .

[17]  Yuan Lou,et al.  Evolution of dispersal in closed advective environments , 2015, Journal of biological dynamics.

[18]  F. Lutscher,et al.  Allee effects and population spread in patchy landscapes , 2015, Journal of biological dynamics.

[19]  Yuan Lou,et al.  Evolution of dispersal in open advective environments , 2013, Journal of Mathematical Biology.

[20]  Boying Wu,et al.  Strong Allee effect in a diffusive predator–prey system with a protection zone☆ , 2014 .

[21]  B. Lou,et al.  Long time behavior of solutions of a reaction–diffusion equation on unbounded intervals with Robin boundary conditions ☆ , 2013, 1309.7441.

[22]  Wan-Tong Li,et al.  Effect of cross-diffusion on the stationary problem of a diffusive competition model with a protection zone , 2013 .

[23]  Yihong Du,et al.  Spreading and vanishing in nonlinear diffusion problems with free boundaries , 2013, 1301.5373.

[24]  C. B. Muratov,et al.  Threshold phenomena for symmetric decreasing solutions of reaction-diffusion equations , 2012, 1203.4623.

[25]  J. Ramírez,et al.  Population persistence under advection–diffusion in river networks , 2011, Journal of mathematical biology.

[26]  P. Cochat,et al.  Et al , 2008, Archives de pediatrie : organe officiel de la Societe francaise de pediatrie.

[27]  Junjie Wei,et al.  Dynamics and pattern formation in a diffusive predator–prey system with strong Allee effect in prey , 2011 .

[28]  Kazuhiro Oeda.  Effect of cross-diffusion on the stationary problem of a prey-predator model with a protection zone , 2011 .

[29]  P. Polácik,et al.  Threshold Solutions and Sharp Transitions for Nonautonomous Parabolic Equations on $${\mathbb{R}^N}$$ , 2011 .

[30]  King-Yeung Lam.  Concentration Phenomena of a Semilinear Elliptic Equation with Large Advection in an Ecological Model , 2010, 1003.5632.

[31]  Yihong Du,et al.  Convergence and sharp thresholds for propagation in nonlinear diffusion problems , 2010 .

[32]  Rui Peng,et al.  Effect of a protection zone in the diffusive Leslie predator-prey model , 2009 .

[33]  P. Polácik.  Threshold solutions and sharp transitions for nonautonomous parabolic equations on R N , 2009 .

[34]  J. Gascoigne,et al.  Allee Effects in Ecology and Conservation , 2008 .

[35]  Luděk Berec,et al.  What are Allee effects , 2008 .

[36]  Yihong Du,et al.  A diffusive competition model with a protection zone , 2008 .

[37]  Yihong Du,et al.  Allee effect and bistability in a spatially heterogeneous predator-prey model , 2007 .

[38]  Henri Berestycki,et al.  Liouville-type results for semilinear elliptic equations in unbounded domains , 2007 .

[39]  Yihong Du,et al.  A diffusive predator–prey model with a protection zone☆ , 2006 .

[40]  Luca Rossi,et al.  On the principal eigenvalue of elliptic operators in $\R^N$ and applications , 2006 .

[41]  Junping Shi,et al.  Persistence in reaction diffusion models with weak allee effect , 2006, Journal of mathematical biology.

[42]  A. Avasthi.  California Tries to Connect Its Scattered Marine Reserves , 2005, Science.

[43]  Andrej Zlatos,et al.  Sharp transition between extinction and propagation of reaction , 2005, math/0504333.

[44]  Yihong Du,et al.  Some Recent Results on Diffusive Predator-prey Models in Spatially Heterogeneous Environment ∗ † , 2005 .

[45]  C. Cosner,et al.  Spatial Ecology via Reaction-Diffusion Equations , 2003 .

[46]  M. Kot,et al.  Integrodifference equations, Allee effects, and invasions , 2002, Journal of mathematical biology.

[47]  Edward O. Wilson,et al.  The Future of Life , 2002 .

[48]  S. B. Blackwell,et al.  Migratory Movements, Depth Preferences, and Thermal Biology of Atlantic Bluefin Tuna , 2001, Science.

[49]  K. Bjorndal,et al.  Historical Overfishing and the Recent Collapse of Coastal Ecosystems , 2001, Science.

[50]  M. Kot,et al.  Speeds of invasion in a model with strong or weak Allee effects. , 2001, Mathematical biosciences.

[51]  R. Holt,et al.  Allee Effects, Invasion Pinning, and Species’ Borders , 2001, The American Naturalist.

[52]  M. Newman,et al.  A model of mass extinction. , 1997, Journal of theoretical biology.

[53]  P. Kareiva,et al.  Allee Dynamics and the Spread of Invading Organisms , 1993 .

[54]  Joachim von Below,et al.  Classical solvability of linear parabolic equations on networks , 1988 .

[55]  D. Aronson,et al.  Multidimensional nonlinear di u-sion arising in population genetics , 1978 .

[56]  L. Peletier,et al.  Nonlinear diffusion in population genetics , 1977 .

[57]  D. Aronson,et al.  Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation , 1975 .

[58]  W. C. Allee.  Animal Aggregations: A Study in General Sociology , 1931 .