西安财经大学数学学院, 陕西 西安 710100
王晶晶(1993年生),女;研究方向:反应扩散系统与斑图动力学;E-mail: jjwang@xaufe.edu.cn
收稿:2026-01-07,
修回:2026-06-01,
录用:2026-06-05,
网络首发:2026-07-08,
移动端阅览
王晶晶. 具有扩散项的最简沉积物模型的Turing-Hopf分支分析[J/OL]. 中山大学学报(自然科学版)(中英文), 2026,1-9.
Wang Jingjing. Turing-Hopf bifurcation analysis of a minimal sediment model with diffusion[J/OL]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2026, 1-9.
王晶晶. 具有扩散项的最简沉积物模型的Turing-Hopf分支分析[J/OL]. 中山大学学报(自然科学版)(中英文), 2026,1-9. DOI: 10.11714/acta.snus.ZR20260006.
Wang Jingjing. Turing-Hopf bifurcation analysis of a minimal sediment model with diffusion[J/OL]. Acta Scientiarum Naturalium Universitatis Sunyatseni, 2026, 1-9. DOI: 10.11714/acta.snus.ZR20260006.
提出了一类带有扩散项的最简沉积物模型. 首先研究了模型Turing-Hopf分支现象的存在性;其次给出了模型在Turing-Hopf分支点处的规范型;最后利用数值结果分析了模型的动力学行为. 研究结果表明,在Turing-Hopf分支点附近,模型呈现出丰富的时空动力学行为,包括空间齐次周期解、空间非齐次周期解以及空间非齐次平衡态解.
A minimal sediment model with diffusion is proposed. Firstly, the existence of Turing-Hopf bifurcation for the model is investigated; Secondly, the normal form of model at the Turing-Hopf bifurcation point is derived; Finally, the dynamics of model are analyzed by means of numerical results. The research indicates that near the Turing-Hopf bifurcation point, the model exhibits rich spatiotemporal dynamics, including the spatially homogeneous periodic solutions, spatially inhomogeneous periodic solutions and spatially inhomogeneous steady-state solutions.
李海侠 , 2017 . 一类扩散食物链模型正解的多重性和唯一性 [J]. 中山大学学报(自然科学版) , 56 ( 5 ): 51 - 59 .
罗丽琴 , 李海侠 , 吴绍艳 , 2025 . 一类具有交错扩散和捕获项的捕食-食饵模型的稳态解 [J]. 中山大学学报(自然科学版中英文) , 64 ( 4 ): 134 - 146 .
王晶晶 , 贾云锋 , 2017 . 一类具有交叉扩散的捕食-食饵模型的共存性 [J]. 中山大学学报(自然科学版) , 56 ( 6 ): 55 - 59 .
Baurmann M , Feudel U , 2004 . Turing patterns in a simple model of a nutrient-microorganism system in the sediment [J]. Ecol Complex , 1 ( 1 ): 77 - 94 .
Cao Q , Wu J H , 2019a . Patterns and dynamics in the diffusive model of a nutrientmicroorganism system in the sediment [J]. Nonlinear Anal Real World Appl , 49 : 331 - 354 .
Cao Q , Wu J H , Wang Y E , 2019b . Bifurcation solutions in the diffusive minimal sediment [J]. Comput Math Appl , 77 ( 3 ): 888 - 906 .
Jia Y F , 2018 . Computational analysis on Hopf bifurcation and stability for a consumer-resource model with nonlinear functional response [J]. Nonlinear Dyn , 94 : 185 - 195 .
Jia Y F , Wang J J , 2025 . Effects of extra resource and harvesting on the pattern formation for a predation system [J]. Commun Nonlinear Sci Numer Simul , 140 : 108381 .
Jiang W H , An Q , Shi J P , 2020 . Formulation of the normal form of Turing-Hopf bifurcation in partial functional differential equations [J]. J Differ Equ , 268 ( 10 ): 6067 - 6102 .
Kovács S , 2004 . Turing bifurcation in a system with cross diffusion [J]. Nonlinear Anal , 59 ( 4 ): 567 - 581 .
Song Y L , Zhang T H , Peng Y H , 2016 . Turing-Hopf bifurcation in the reaction-diffusion equations and its applications [J]. Commun Nonlinear Sci Numer Simul , 33 : 229 - 258 .
Wang J J , Jia Y F , Shi M J , 2024 . Existence and Turing instability of positive solutions for a predator-pest model with additional food [J]. Appl Math Lett , 157 : 109191 .
Wang J J , Zheng H C , Jia Y F , 2021 . Dynamical analysis on a bacteria-phages model with delay and diffusion [J]. Chaos Solitons Fractals , 143 : 110597 .
Wu H , Song B , Zhang L , et al , 2026 . Turing-Hopf bifurcation and inhomogeneous pattern for a reaction-diffusion SIR epidemic model with chemotaxis and delay [J]. Math Comput Simul , 240 : 1000 - 1022 .
Xing Y , Jiang W H , 2024 . Turing-Hopf bifurcation and bi-stable spatiotemporal periodic orbits in a delayed predator-prey model with predator-taxis [J]. J Math Anal Appl , 533 ( 1 ): 127994 .
Xu X F , Wei J J , 2018 . Turing-Hopf bifurcation of a class of modified Leslie-Gower model with diffusion [J]. Discrete Contin Dyn Syst B , 23 ( 2 ): 765 - 783 .
Yi F Q , Gaffney E A , Seirin-Lee S , 2017 . The bifurcation analysis of Turing pattern formation induced by delay and diffusion in the Schnakenberg system [J]. Discrete Contin Dyn Syst B , 22 ( 2 ): 647 - 668 .
0
浏览量
0
下载量
0
CSCD
关联资源
相关文章
相关作者
相关机构
京公网安备11010802024621
