Propagation dynamics in periodic predator-prey systems with nonlocal dispersal

Alikakos, 1999, Periodic traveling waves and locating oscillating patterns in multidimensional domains, Trans. Am. Math. Soc., 351, 2777, 10.1090/S0002-9947-99-02134-0 Andreu, 2008, A nolocal p-Laplacian evolution equation with Neumann boundary conditions, J. Math. Pures Appl., 90, 201, 10.1016/j.matpur.2008.04.003 Banaś, 1980, On measures of noncompactness in Banach spaces, Comment. Math. Univ. Carol., 21, 131 Bates, 2006, On some nonlocal evolution equations arising in materials science, vol. 48, 13 Bates, 1999, Periodic traveling waves for a nonlocal integro-differential model, Electron. J. Differ. Equ., 26, 1 Berestycki, 1994, The principal eigenvalue and maximum principle for second-order elliptic operators in general domains, Commun. Pure Appl. Math., 47, 47, 10.1002/cpa.3160470105 Berestycki, 2016, On the definition and the properties of the principal eigenvalue of some nonlocal operators, J. Funct. Anal., 271, 2701, 10.1016/j.jfa.2016.05.017 Carrère, 2018, Spreading speeds for a two-species competition-diffusion system, J. Differ. Equ., 264, 2133, 10.1016/j.jde.2017.10.017 Chasseigne, 2006, Asymptotic behavior for nonlocal diffusion equations, J. Math. Pures Appl., 86, 271, 10.1016/j.matpur.2006.04.005 Coville, 2020, On generalized principal eigenvalues of nonlocal operators with a drift, Nonlinear Anal., 193, 1, 10.1016/j.na.2019.07.002 Cushing, 1977, Periodic time-dependent predator-prey systems, SIAM J. Appl. Math., 32, 82, 10.1137/0132006 Deimling, 1985 Ducrot, 2013, Convergence to generalized transition waves for some Holling-Tanner prey-predator reaction-diffusion system, J. Math. Pures Appl., 100, 1, 10.1016/j.matpur.2012.10.009 Ducrot, 2016, Spatial propagation for a two component reaction-diffusion system arising in population dynamics, J. Differ. Equ., 260, 8316, 10.1016/j.jde.2016.02.023 Ducrot, 2019, Spreading speeds for multidimensional reaction-diffusion systems of the prey-predator type, Calc. Var. Partial Differ. Equ., 137, 1 Fang, 2010, Existence and uniqueness of traveling waves for non-monotone integral equations with applications, J. Differ. Equ., 248, 2199, 10.1016/j.jde.2010.01.009 Fang, 2015, Bistable traveling waves for monotone semiflows with applications, J. Eur. Math. Soc., 17, 2243, 10.4171/JEMS/556 Fife, 1977, The approach of solutions of nonlinear diffusion equations to travelling front solutions, Arch. Ration. Mech. Anal., 65, 335, 10.1007/BF00250432 Garcia-Melián, 2009, On the principal eigenvalue of some nonlocal diffusion problems, J. Differ. Equ., 246, 21, 10.1016/j.jde.2008.04.015 Hale, 1973, Fixed point theorems and dissipative processes, J. Differ. Equ., 13, 391, 10.1016/0022-0396(73)90025-9 Hao, 2021, Traveling waves in a nonlocal dispersal predator-prey model, Discrete Contin. Dyn. Syst., Ser. S, 14, 3113 Hsu, 2008, Spreading speeds and traveling waves for nonmonotone integrodifference equations, SIAM J. Math. Anal., 40, 776, 10.1137/070703016 Hsu, 2011, Dynamics of a periodically pulsed bio-reactor model with a hydraulic storage zone, J. Dyn. Differ. Equ., 23, 817, 10.1007/s10884-011-9224-3 Jin, 2009, Spatial dynamics of a periodic population model with dispersal, Nonlinearity, 22, 1167, 10.1088/0951-7715/22/5/011 Li, 2020, Propagation dynamics in a time periodic nonlocal dispersal model with stage structure, J. Dyn. Differ. Equ., 32, 1027, 10.1007/s10884-019-09760-3 Liang, 2006, Spreading speeds and traveling waves for periodic evolution system, J. Differ. Equ., 231, 57, 10.1016/j.jde.2006.04.010 Liu, 2020, Asymptotic spreading of interacting species with multiple fronts I: a geometric optics approach, Discrete Contin. Dyn. Syst., 40, 3683, 10.3934/dcds.2020050 Magal, 2005, Global attractors and steady states for uniformly persistent dynamical systems, SIAM J. Math. Anal., 37, 251, 10.1137/S0036141003439173 Murray, 2003 Nathan, 2012, Dispersal kernels: review, 187 Nussbaum, 1972, Some asymptotic fixed point theorems, Trans. Am. Math. Soc., 171, 349, 10.1090/S0002-9947-1972-0310719-6 Okubo, 2001 Poláčik, 2020, Propagating terraces and the dynamics of front-like solutions of reaction-diffusion equations on R, Mem. Am. Math. Soc., 264, 1 Rawal, 2012, Criteria for the existence and lower bounds of principal eigenvalues of time periodic nonlocal dispersal operators and applications, J. Dyn. Differ. Equ., 24, 927, 10.1007/s10884-012-9276-z Rinaldi, 1993, Multiple attractors, catastrophes and chaos in seasonally perturbed predator-prey communities, Bull. Math. Biol., 55, 15, 10.1016/S0092-8240(05)80060-6 Sell, 2002 Sherratt, 2016, Invasion generates periodic traveling waves (wavetrains) in predator-prey models with nonlocal dispersal, SIAM J. Appl. Math., 76, 293, 10.1137/15M1027991 Su, 2020, The generalised principal eigenvalue of time-periodic nonlocal dispersal operators and applications, J. Differ. Equ., 269, 4960, 10.1016/j.jde.2020.03.046 Sun, 2017, The periodic principal eigenvalues with applications to the nonlocal dispersal logistic equation, J. Differ. Equ., 263, 934, 10.1016/j.jde.2017.03.001 Taylor, 2013, Seasonal forcing and multi-year cycles in interacting populations: lessons from a predator-prey model, J. Math. Biol., 67, 1741, 10.1007/s00285-012-0612-z Wang, 2011, Spreading speeds and traveling waves for non-cooperative reaction-diffusion systems, J. Nonlinear Sci., 21, 747, 10.1007/s00332-011-9099-9 Weinberger, 2009, Spreading speeds for a partially cooperative 2-species reaction-diffusion model, Discrete Contin. Dyn. Syst., 23, 1087, 10.3934/dcds.2009.23.1087 Weng, 2006, Spreading speed and traveling waves for a multi-type SIS epidemic model, J. Differ. Equ., 229, 270, 10.1016/j.jde.2006.01.020 Wu, 2015, Global attractivity, spreading speeds and traveling waves of delayed nonlocal reaction-diffusion systems, J. Differ. Equ., 258, 1058, 10.1016/j.jde.2014.10.009 Zhang, 2020, Propagation phenomena for a two-species Lotka-Volterra strong competition system with nonlocal dispersal, Calc. Var. Partial Differ. Equ., 59, 3, 10.1007/s00526-019-1662-5 Wang, 2018, Time periodic traveling waves for a periodic and diffusive SIR epidemic model, J. Dyn. Differ. Equ., 30, 379, 10.1007/s10884-016-9546-2 Zhang, 2019, Propagation dynamics of a time periodic and delayed reaction-diffusion model without quasi-monotonicity, Trans. Am. Math. Soc., 372, 1751, 10.1090/tran/7709 Zhang, 2020, Time periodic traveling wave solutions for a Kermack-McKendrick epidemic model with diffusion and seasonality, J. Evol. Equ., 20, 1029, 10.1007/s00028-019-00544-2 Zhao, 2011, Existence, uniqueness and asymptotic stability of time periodic traveling waves for a periodic Lotka-Volterra competition system with diffusion, J. Math. Pures Appl., 95, 627, 10.1016/j.matpur.2010.11.005 Zhao, 2014, Time periodic traveling wave solutions for periodic advection-reaction-diffusion systems, J. Differ. Equ., 257, 1078, 10.1016/j.jde.2014.05.001 Zhao, 2015, The decay rates of traveling waves and spectral analysis for a class of nonlocal evolution equations, Math. Model. Nat. Phenom., 10, 142, 10.1051/mmnp/20150610 Zhao, 2018, Spatial and temporal dynamics of a nonlocal viral infection model, SIAM J. Appl. Math., 78, 1954, 10.1137/17M1144106 Zhao, 2017