Dynamics of a Nonlocal Dispersal Model with a Nonlocal Reaction Term

In this paper, we study a class of nonlocal dispersal problem with a nonlocal term arising in population dynamics: ut = 𝒟u + u λ − f(u) −∫ΩK(x,y)g(u(y))dy,in Ω × (0, +∞), u(x, 0) = u0(x) ≥ 0, in Ω,...

[1]  Junping Shi,et al.  Existence and uniqueness of steady state solutions of a nonlocal diffusive logistic equation , 2013 .

[2]  Wan-Tong Li,et al.  A nonlocal dispersal logistic equation with spatial degeneracy , 2015 .

[3]  Wenxian Shen,et al.  Spreading speeds for monostable equations with nonlocal dispersal in space periodic habitats , 2010 .

[4]  L. Birch,et al.  Experimental Background to the Study of the Distribution and Abundance of Insects: I. The Influence of Temperature, Moisture and Food on the Innate Capacity for Increase of Three Grain Beetles , 1953 .

[5]  Wan-Tong Li,et al.  Approximate the FokkerPlanck equation by a class of nonlocal dispersal problems , 2011 .

[6]  Zhi-Cheng Wang,et al.  Entire solutions in nonlocal dispersal equations with bistable nonlinearity , 2011 .

[7]  Juncheng Wei,et al.  On a nonlocal Eigenvalue Problem and its Applications to Point-condensations in reaction-Diffusion Systems , 2000, Int. J. Bifurc. Chaos.

[8]  Shangjiang Guo,et al.  Patterns in a nonlocal time-delayed reaction–diffusion equation , 2018 .

[9]  Li Ma,et al.  Stability and Bifurcation in a Delayed Reaction–Diffusion Equation with Dirichlet Boundary Condition , 2016, J. Nonlinear Sci..

[10]  Yuan Lou,et al.  Random dispersal vs. non-local dispersal , 2009 .

[11]  Wan-Tong Li,et al.  Entire solutions in the Fisher-KPP equation with nonlocal dispersal , 2010 .

[12]  Shangjiang Guo,et al.  Stability analysis of a stage structure model with spatiotemporal delay effect , 2017, Comput. Math. Appl..

[13]  Yuan Lou,et al.  Evolution of Mixed Dispersal in Periodic Environments , 2012 .

[14]  Wendell H. Fleming,et al.  A selection-migration model in population genetics , 1975 .

[15]  Shangjiang Guo,et al.  Bifurcation and stability of a Mimura–Tsujikawa model with nonlocal delay effect , 2016 .

[16]  Julio D. Rossi,et al.  Maximum and antimaximum principles for some nonlocal diffusion operators , 2009 .

[17]  Julio D. Rossi,et al.  A logistic equation with refuge and nonlocal diffusion , 2009 .

[18]  Shoji Yotsutani.  On a Limiting System in the Lotka-Volterra Competition with Cross-Diffusion (Nonlinear Diffusive Systems and Related Topics) , 2002 .

[19]  Noemi Wolanski,et al.  Boundary fluxes for nonlocal diffusion , 2007 .

[20]  Wenxian Shen,et al.  Stationary solutions and spreading speeds of nonlocal monostable equations in space periodic habitats , 2012 .

[21]  V. Hutson,et al.  The evolution of dispersal , 2003, Journal of mathematical biology.

[22]  Wan-Tong Li,et al.  Travelling wave fronts in nonlocal delayed reaction-diffusion systems and applications , 2009 .

[23]  S. Varadhan,et al.  On a variational formula for the principal eigenvalue for operators with maximum principle. , 1975, Proceedings of the National Academy of Sciences of the United States of America.

[24]  Peter W. Bates,et al.  Existence, uniqueness and stability of the stationary solution to a nonlocal evolution equation arising in population dispersal , 2007 .

[25]  P. Bates,et al.  Traveling Waves in a Convolution Model for Phase Transitions , 1997 .

[26]  Daniel Escaff,et al.  Self-Replication and Localized Structures Interaction in a Nonlocal Model of Population Dynamics , 2009, Int. J. Bifurc. Chaos.

[27]  Julio D. Rossi,et al.  On the principal eigenvalue of some nonlocal diffusion problems , 2009 .

[28]  Shangjiang Guo,et al.  Hopf bifurcation in a diffusive Lotka–Volterra type system with nonlocal delay effect , 2016 .

[29]  J. Coville.  On a simple criterion for the existence of a principal eigenfunction of some nonlocal operators , 2010, 1106.5137.

[30]  Wan-Tong Li,et al.  A nonlocal dispersal equation arising from a selection-migration model in genetics , 2014 .

[31]  Wan-Tong Li,et al.  Asymptotic behavior for nonlocal dispersal equations , 2010 .

[32]  Yuan Lou,et al.  Diffusion, Self-Diffusion and Cross-Diffusion , 1996 .

[33]  Li Ma,et al.  Stability and bifurcation in a diffusive Lotka-Volterra system with delay , 2016, Comput. Math. Appl..

[34]  Julián López-Gómez,et al.  First Variations of Principal Eigenvalues with Respect to the Domain and Point-Wise Growth of Positive Solutions for Problems Where Bifurcation from Infinity Occurs , 1998 .

[35]  Shangjiang Guo,et al.  Bifurcation and spatio-temporal patterns in a diffusive predator–prey system , 2018, Nonlinear Analysis: Real World Applications.

[36]  Jim Hone,et al.  Population growth rate and its determinants: an overview. , 2002, Philosophical transactions of the Royal Society of London. Series B, Biological sciences.

[37]  Emmanuel Chasseigne,et al.  Asymptotic behavior for nonlocal diffusion equations , 2006 .

[38]  M. Grinfeld,et al.  Local vs. non-local interactions in population dynamics , 1989 .

[39]  Wenxian Shen,et al.  Criteria for the Existence and Lower Bounds of Principal Eigenvalues of Time Periodic Nonlocal Dispersal Operators and Applications , 2012 .

[40]  Paul C. Fife,et al.  Some Nonclassical Trends in Parabolic and Parabolic-like Evolutions , 2003 .

[41]  Shangjiang Guo,et al.  Spatio-temporal patterns in a diffusive model with non-local delay effect , 2017 .

[42]  Shangjiang Guo,et al.  Stability and bifurcation in a reaction-diffusion model with nonlocal delay effect , 2015 .

[43]  Noemi Wolanski,et al.  How to Approximate the Heat Equation with Neumann Boundary Conditions by Nonlocal Diffusion Problems , 2006, math/0607058.

[44]  Jérôme Coville,et al.  Existence and Uniqueness of Solutions to a Nonlocal Equation with Monostable Nonlinearity , 2008, SIAM J. Math. Anal..

[45]  Rong Zou,et al.  Bifurcation of Reaction Cross-Diffusion Systems , 2017, Int. J. Bifurc. Chaos.

[46]  Michael G. Crandall,et al.  Bifurcation, perturbation of simple eigenvalues, itand linearized stability , 1973 .

[47]  Rong Zou,et al.  Dynamics in a diffusive predator-prey system with ratio-dependent predator influence , 2017, Comput. Math. Appl..