一类格竞争系统的双稳周期行波解

李俭

doi:10.21656/1000-0887.430071

一类格竞争系统的双稳周期行波解

doi: 10.21656/1000-0887.430071

李俭

西安电子科技大学数学与统计学院，西安 710071

详细信息

作者简介:
李俭(1998—), 男, 硕士(E-mail: 2084043762@qq.com)

中图分类号: O175.14
计量
- 文章访问数: 250
- HTML全文浏览量: 115
- PDF下载量: 43
- 被引次数: 0
出版历程
- 收稿日期: 2022-03-07
- 修回日期: 2022-04-11
- 刊出日期: 2023-04-01

Bistable Periodic Traveling Wave Solutions to Lattice Competitive Systems

LI Jian

School of Mathematics and Statistics, Xidian University, Xi'an 710071, P.R.China

摘要

摘要: 该文研究了一类格竞争系统的双稳周期行波解的存在性.首先, 将两种群竞争系统转化为合作系统；其次, 构造合作系统的上下解, 并建立比较原理, 得到当初始函数满足一定条件时, 解在无穷远处是收敛的；最后, 利用黏性消去法证明系统连接两个稳定周期平衡点的行波解的存在性.
- 格竞争系统 /
- 双稳周期行波解 /
- 比较原理 /
- 黏性消去法
Abstract: The existence of bistable periodic traveling wave solutions to lattice competitive systems was studied. Firstly, the lattice competitive system of 2 species was transformed into a cooperative system. Then, the principle of comparison was established and a pair of upper and lower solutions were given to obtain the convergence of the solution at infinity, with the initial function satisfying certain conditions. By means of the vanishing viscosity method and the principle of comparison, the existence of the traveling wave solution connecting 2 stable periodic equilibrium points of the system, was proved.
- lattice competitive system /
- bistable periodic traveling wave /
- principle of comparison /
- vanishing viscosity method

HTML全文

参考文献(18)

[1]	BAO X X, WANG Z C. Existence and stability of time periodic traveling waves for a periodic bistable Lotka-Volterra competition system[J]. Journal of Differential Equations, 2013, 255: 2402-2435. doi: 10.1016/j.jde.2013.06.024
[2]	FANG J, ZHAO X Q. Monotone wavefronts for partially degenerate reaction-diffusion systems[J]. Journal of Dynamics and Differential Equations, 2009, 21: 663-680. doi: 10.1007/s10884-009-9152-7
[3]	LI B. Traveling wave solutions in partially degenerate cooperative reaction-diffusion systems[J]. Journal of Differential Equations, 2012, 252(9): 4842-4861. doi: 10.1016/j.jde.2012.01.018
[4]	ZHAO G Y, RUAN S G. Existence, uniqueness and asymptotic stability of time periodic traveling waves for a periodic Lotka-Volterra competition system with diffusion[J]. Journal de Mathématiques Pures et Appliquées, 2011, 95(6): 627-671. doi: 10.1016/j.matpur.2010.11.005
[5]	HAO Y X, LI W T, WANG J B. Propagation dynamics of Lotka-Volterra competition systems with asymmetric dispersal in periodic habits[J]. Journal of Differential Equations, 2021, 300: 185-225. doi: 10.1016/j.jde.2021.07.041
[6]	BAO X X, LI W T, WANG Z C. Time periodic traveling curved fronts in the periodic Lotka-Volterra competition diffusion system[J]. Journal of Dynamics and Differential Equations, 2017, 29: 981-1016. doi: 10.1007/s10884-015-9512-4
[7]	GUO J S, WU C H. Wave propagation for a two-component lattice dynamical system arising in strong competition models[J]. Journal of Differential Equations, 2011, 250: 3504-3533. doi: 10.1016/j.jde.2010.12.004
[8]	GUO J S, WU C H. Traveling wave front for a two-component lattice dynamical system arising in competition models[J]. Journal of Differential Equations, 2012, 252: 4357-4391. doi: 10.1016/j.jde.2012.01.009
[9]	WANG H Y, OU C H. Propagation direction of the traveling wave for the Lotka-Volterra competitive lattice system[J]. Journal of Dynamics and Differential Equations, 2021, 33: 1153-1174. doi: 10.1007/s10884-020-09853-4
[10]	SHEN W X. Traveling waves in time periodic lattice differential equations[J]. Nonlinear Analysis, 2003, 54(2): 319-339. doi: 10.1016/S0362-546X(03)00065-8
[11]	ZHANG K F, ZHAO X Q. Spreading speed and traveling waves for a spatially discrete SIS epidemic model[J]. Nonlinearity, 2008, 21(1): 97-112. doi: 10.1088/0951-7715/21/1/005
[12]	KRUXZKOV S N. First order quasilinear equations in several independent variables[J]. Mathematics of the USSR-Sbornik, 1970, 10: 217-243. doi: 10.1070/SM1970v010n02ABEH002156
[13]	GUO J S, HAMEL F. Front propagation for discrete periodic monostable equations[J]. Mathematische Annalen, 2006, 335: 489-525. doi: 10.1007/s00208-005-0729-0
[14]	CHEN X F, GUO J S, WU C C. Traveling waves in discrete periodic media for bistable dynamics[J]. Archive for Rational Mechanics and Analysis, 2008, 189: 189-236. doi: 10.1007/s00205-007-0103-3
[15]	陈妍. 时间周期的离散SIS模型的传播动力学[J]. 应用数学和力学, 2022, 43(10): 1155-1163. doi: 10.21656/1000-0887.420350 CHEN Yan. Propagation dynamics of a discrete SIS model with time periodicity[J]. Applied Mathematics and Mechanics, 2022, 43(10): 1155-1163. (in Chinese) doi: 10.21656/1000-0887.420350
[16]	郑景盼. 三物种竞争-扩散系统双稳行波解的波速符号[J]. 应用数学和力学, 2021, 42(12): 1296-1305. doi: 10.21656/1000-0887.420093 ZHENG Jingpan. The wave speed signs for bistable traveling wave solutions in 3-species competition-diffusion systems[J]. Applied Mathematics and Mechanics, 2021, 42(12): 1296-1305. (in Chinese) doi: 10.21656/1000-0887.420093
[17]	SHEN W X. Traveling waves in time almost periodic structures governed by bistable nonlinearities, Ⅱ: existence[J]. Journal of Differential Equations, 1999, 159(1): 55-101. doi: 10.1006/jdeq.1999.3652
[18]	WU S L, HSU C H. Periodic traveling fronts for partially degenerate reaction-diffusion systems with bistable and time-periodic nonlinearity[J]. Advances in Nonlinear Analysis, 2020, 9: 923-957.