JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (4): 40-49.doi: 10.6040/j.issn.1671-9352.0.2024.184

Previous Articles    

Stability of bistable waves for a class of system with asymmetric and nonlocal dispersal

LI Siyu, YANG Yunrui*   

  1. School of Mathematics and Physics, Lanzhou Jiaotong University, Lanzhou 730070, Gansu, China
  • Published:2025-04-08

PDF (PC)

54

Abstract: This paper considers the stability of bistable traveling wave solutions for a class of system with asymmetric and nonlocal dispersal. On the basis of the existence of bistable waves, the global stability of bistable waves is obtained with the help of the method of super-and sub-solutions combining with the convergence results of monotone semiflows. Then, the uniqueness of bistable waves is established by using the analysis techniques.

Key words: asymmetric and nonlocal dispersal, bistable traveling waves, stability

CLC Number: 

  • O175
[1] 叶其孝,李正元,王明新,等. 反应扩散方程引论[M]. 2版. 北京:科学出版社,2011. YE Qixiao, LI Zhengyuan, WANG Mingxin, et al. Introduction to reaction-diffusion equations [M]. 2nd ed. Beijing: Science Press, 2011.
[2] HSU C H, YANG T S. Existence, uniqueness, monotonicity and asymptotic behaviour of travelling waves for epidemic models [J]. Nonlinearity, 2013, 26:121-139.
[3] ARONSON D G, WEINBERGER H F. Nonlinear diffusion in population genetics, combustion, and nerve pulse propagation[M] //Lecture Notes in Mathematics. Berlin:Springer, 1975:5-49.
[4] BATES P W, FIFE P C, REN Xiao feng, et al. Traveling waves in a convolution model for phase transitions[J]. Archive for Rational Mechanics and Analysis, 1997, 138(2):105-136.
[5] YU Zhixian, WAN Yuji, HSU Cheng-hsiung. Wave propagation and its stability for a class of discrete diffusion systems[J]. Zeitschrift Für Angewandte Mathematik und Physik, 2020, 71(6):194.
[6] XU Dashun, ZHAO Xiaoqiang. Bistable waves in an epidemic model[J]. Journal of Dynamics and Differential Equations, 2004, 16(3):679-707.
[7] 吴事良. 非局部时滞反应扩散方程的行波解和渐近传播速度[D]. 西安:西安电子科技大学,2009. WU Shiliang. Traveling wave solutions and asymptotic propagation velocity of nonlocal delay reaction-diffusion equations[D]. Xian:Xidian University, 2009
[8] COVILLE Jérôme, DUPAIGNE Louis. Propagation speed of travelling fronts in non local reaction-diffusion equations[J]. Nonlinear Analysis: Theory, Methods & Applications, 2005, 60(5):797-819.
[9] COVILLE Jérôme. On uniqueness and monotonicity of solutions of non-local reaction diffusion equation[J]. Annali Di Matematica Pura Ed Applicata, 2006, 185(3):461-485.
[10] 李孝武,杨赟瑞,刘凯凯. 一类时滞非局部扩散SVIR模型单稳行波解的稳定性[J]. 浙江大学学报(理学版),2023,50(3):273-286. LI Xiaowu, YANG Yunrui, LIU Kaikai. Stability of monostable traveling waves for a class of SVIR models with nonlocal diffusion and delay[J]. Journal of Zhejiang University(Science Edition), 2023, 50(3):273-286.
[11] ZHANG Guobao, ZHAO Xiaoqiang. Propagation phenomena for a two-species Lotka-Volterra strong competition system with nonlocal dispersal[J]. Calculus of Variations and Partial Differential Equations, 2019, 59(1):10.
[12] 郝玉财. 两类非局部扩散系统行波解的稳定性[D]. 兰州:西北师范大学,2022. HAO Yucai. Stability of traveling wave solutions for two kinds of nonlocal diffusion systems[D]. Lanzhou:Northwest Normal University, 2022.
[13] CHEN Xinfu. Existence, uniqueness and asymptotic stability of traveling waves in nonlocal evolution equations[J]. Advances in Differential Equations, 1997, 2(1):125-160.
[14] HAO Yucai, ZHANG Guobao. Global stability of bistable traveling wavefronts for a three-species Lotka-Volterra competition system with nonlocal dispersal[J]. International Journal of Biomathematics, 2023, 16(5):22250106.
[15] LIU Kaikai, YANG Yunrui. Global stability of traveling waves for a SIR model with nonlocal dispersal and delay[J]. Journal of Mathematical Physics, 2022, 63(2):021504.
[16] YANG Lu, YANG Yunrui, SONG Xue. Traveling waves in a SIRH model with spatio-temporal delay and nonlocal dispersal[J]. Acta Mathematica Scientia, 2022, 42(2):715-736.
[17] COVILLE Jérôme. Travelling fronts in asymmetric nonlocal reaction diffusion equations: the bistable and ignition cases[J]. Prépublication du CMM, Hal-00696208.
[18] COVILLE Jérôme, DÁVILA Juan, MARTÍNEZ Salomé. Nonlocal anisotropic dispersal with monostable nonlinearity[J]. Journal of Differential Equations, 2008, 244(12):3080-3118.
[19] LI Wantong, XU Wenbing, ZHANG Liang. Traveling waves and entire solutions for an epidemic model with asymmetric dispersal[J]. Discrete and Continuous Dynamical Systems, 2017, 37(5):2483-2512.
[20] HU Ruyue, LI Wantong, XU Wenbing. Propagation phenomena for man-environment epidemic model with nonlocal dispersals[J]. Journal of Nonlinear Science, 2022, 32(5):67.
[21] 杨璐. 两类时滞非局部扩散传染病系统的行波解研究[D]. 兰州:兰州交通大学,2022. YANG Lu. Study on traveling wave solutions of two kinds of non-local diffusion infectious disease systems with time delay[D]. Lanzhou: Lanzhou Jiatong University, 2022.
[22] WENG Peixuan, ZHAO Xiaoqiang. Spreading speed and traveling waves for a multi-type SIS epidemic model[J]. Journal of Differential Equations, 2006, 229(1):270-296.
[23] 王高雄. 常微分方程[M]. 3版. 北京:高等教育出版社,2006. Wang Gaoxiong. Ordinary differential equation[M]. 3rd ed. Beijing: Higher Education Press, 2006.
[24] ZHAO Xiaoqiang. Dynamical systems in population biology[M]. New York: Springer, 2003.
[1] MAI Ali, SUN Guowei. Stability analysis of predator-prey metacommunity model with predator dispersal between patches [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(4): 20-28.
[2] Wenhui DU,Xiangtuan XIONG. Iterated fractional Tikhonov method for simultaneous inversion of the source term and initial data in time-fractional diffusion equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(8): 77-83.
[3] Hui MIAO,Xamxinur ABDURAHMAN. Dynamic behaviors analysis of delayed HIV model with cell-to-cell transmissions and protease inhibitors [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(4): 90-97.
[4] Zheng XIN,Dingguo WANG,Tiwei ZHAO. Stability function and torsion theory on exact categories [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(2): 105-109.
[5] Yiyan WANG,Dongxia ZHAO,Caixia GAO. On ramp control of ARZ traffic flow model based on time-delay feedback [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(10): 64-73, 88.
[6] Yuling LIU. Structured backward error for a class of generalized saddle point problems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(10): 40-45.
[7] ALI Adil,RAHMAN Kaysar. Differential quadrature method for solving the generalized Burgers-Fisher equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2024, 59(10): 30-39.
[8] Yadi WANG,Hailong YUAN. Hopf bifurcation analysis in the Lengyel-Epstein reaction diffusion system with time delay [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(8): 92-103.
[9] Yun NI,Xiping LIU. Existence and Ulam stability for positive solutions of conformable fractional coupled systems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(8): 82-91.
[10] Zipeng HE,Yaying DONG. Steady-state solutions of a Holling type Ⅱ competition model in heterogeneous environment [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(8): 73-81.
[11] Yuwen HU,Jiucheng XU,Qianqian ZHANG. Lyapunov stability of decision evolution set [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(7): 52-59.
[12] Yun LIU,Pengjun ZHU,Luyao CHEN,Kai SONG. Optimization of blockchain sharding by profit incentive algorithm based on edge computing [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(7): 88-96.
[13] HUANG Yu, GAO Guang-hua. Compact difference schemes for the fourth-order parabolic equations with the third Dirichlet boundary [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(4): 16-28.
[14] Gaihui GUO,Jingjing WANG,Wangrui LI. Hopf bifurcation of a vegetation-water reaction-diffusion model with time delay [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(10): 32-42, 53.
[15] Yonghua LI,Cunhua ZHANG. Stability of a single population delayed reaction-diffusion model with Dirichlet boundary condition [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(10): 122-126.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd