Front-Like Entire Solutions to Lattice Periodic Dynamic Systems With Delays and Global Interaction
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摘要: 研究了一类一维空间周期格上的具有时滞和全局交互作用的微分系统的front-like整体解.通过建立适当的比较原理,并融合不同方向的波前解与连接稳定态和不稳定态的空间周期解,构造了front-like整体解并证明了一些定性性质.与波前解相比,front-like整体解能够展示出新的动力学行为.
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关键词:
- 周期格动力系统 /
- 空间周期解 /
- front-like整体解 /
- 比较原理
Abstract: 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. -
[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 RN [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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