XUE Xue. Front-Like Entire Solutions to Lattice Periodic Dynamic Systems With Delays and Global Interaction[J]. Applied Mathematics and Mechanics, 2020, 41(2): 223-234. doi: 10.21656/1000-0887.400170
Citation: XUE Xue. Front-Like Entire Solutions to Lattice Periodic Dynamic Systems With Delays and Global Interaction[J]. Applied Mathematics and Mechanics, 2020, 41(2): 223-234. doi: 10.21656/1000-0887.400170

Front-Like Entire Solutions to Lattice Periodic Dynamic Systems With Delays and Global Interaction

doi: 10.21656/1000-0887.400170
Funds:  The National Natural Science Foundation of China(11671315)
  • Received Date: 2019-05-15
  • Publish Date: 2020-02-01
  • The front-like entire solutions to lattice periodic dynamic systems with delays and global interaction were investigated. Through establishment of appropriate comparison theorems, some front-like entire solutions were constructed out of mixture of the traveling fronts with different directions of propagation and spatially periodic solutions connecting unstable equilibrium and stable equilibrium. Some properties of these entire solutions were also discussed. The front-like entire solutions, exhibiting new characteristic behaviors in the front dynamics, are different from the traveling fronts.
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  • [1]
    WENG P X, HUANG H X, WU J H. Asymptotic speed of propagation of wave fronts in a lattice delay differential equation with global interaction[J].IMA Journal of Applied Mathematics,2003,〖STHZ〗 68(4): 409-439.
    [2]
    WU S L, HSU C H. Propagation of monostable traveling fronts in discrete periodic media with delay[J]. Discrete Continuous Dynamic System,2018,38(6): 3025-3060.
    [3]
    EI S I. The motion of weakly interacting pulses in reaction-diffusion systems[J]. Journal of Dynamics and Differential Equations,2002,14(1):85-137.
    [4]
    EI S I, MIMURA M, NAGAYAMA M. Pulse-pulse interaction in reaction-diffusion systems[J]. Physica D: Nonlinear Phenomena,2002,〖STHZ〗 165(3): 176-198.
    [5]
    KAWAHARA T, TANAKA M. Interactions of traveling fronts: an exact solution of a nonlinear diffusion equation[J]. Physics Letters A,1983,97(8): 311-314.
    [6]
    GUO J S, MORITA Y. Entire solutions of reaction-diffusion equations and an application to discrete diffusive equations[J]. Discrete Continuous Dynamic System,2005,12(2): 193-212.
    [7]
    HAMEL F, NADIRASHVILI N. Entire solutions of the KPP equation[J]. Communications on Pure and Applied Mathematics,1999,52(10): 1255-1276.
    [8]
    HAMEL F, NADIRASHVILI N. Travelling fronts and entire solutions of the Fisher-KPP equation in RN [J]. Archive for Rational Mechanics and Analysis,2001,157(2): 91-163.
    [9]
    LI W T, LIU N W, WANG Z C. Entire solutions in reaction-advection-diffusion equations in cylinders[J]. Journal de Mathématiques Pures et Appliqués,2008,90(5): 492-504.
    [10]
    LIU N W, LI W T AND WANG Z C. Entire solutions of reaction-advection-diffusion equations with bistable nonlinearity in cylinders[J]. Journal of Differential Equations,2009,246(11): 4249-4267.
    [11]
    MORITA Y, NINOMIYA H. Entire solutions with merging fronts to reaction-diffusion equations[J]. Journal of Dynamics and Differential Equations,2006,18(4): 841-861.
    [12]
    LI W T, WANG Z C, WU J H. Entire solutions in monostable reaction-diffusion equations with delayed nonlinearity[J]. Journal of Differential Equations,2008,245(1): 102-129.
    [13]
    WANG Z C, LI W T, RUAN S G. Entire solutions in bistable reaction-diffusion equations with nonlocal delayed nonlinearity[J]. Transactions of the American Mathematical Society,2009,361(4): 2047-2084.
    [14]
    WANG Z C, LI W T, WU J H. Entire solutions in delayed lattice differential equations with monostable nonlinearity[J]. SIAM Journal on Mathematical Analysis,2009,40(6): 2392-2420.
    [15]
    WANG Z C, LI W T, RUAN S G. Entire solutions in lattice delayed differential equations with nonlocal interaction: bistable case[J]. Mathematical Modelling of Natural Phenomena,2013,8(3): 78-103.
    [16]
    SUN Y J, LI W T, WANG Z C. Entire solutions in nonlocal dispersal equations with bistable nonlinearity[J]. Journal of Differential Equations,2011,251(3): 551-581.
    [17]
    WU S L, HSU C H. Entire solutions of nonlinear cellular neural networks with distributed time delays[J]. Nonlinearity,2012,〖STHZ〗 25(9): 1-17.
    [18]
    MORITA Y, TACHIBANA K. An entire solution to the Lotka-Volterra competition-diffusion equations[J]. SIAM Journal on Mathematical Analysis,2009,40(6): 2217-2240.
    [19]
    WANG M X, L G Y. Entire solutions of a diffusive and competitive Lotka-Volterra type system with nonlocal delay[J]. Nonlinearity,2010,23(7): 1609-1630.
    [20]
    WU S L, WANG H Y. Front-like entire solutions for monostable reaction-diffusion systems[J]. Journal of Dynamics and Differential Equations,2013,25(2): 505-533.
    [21]
    WU S L, SHI Z X, YANG F Y. Entire solutions in periodic lattice dynamical systems[J]. Journal of Differential Equations,2013,255(10): 3505-3535.
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