数学
特征向量
吸引子
领域(数学分析)
耗散系统
简并能级
分叉
简单(哲学)
数学分析
物理
非线性系统
量子力学
认识论
哲学
出处
期刊:Discrete and Continuous Dynamical Systems-series B
[American Institute of Mathematical Sciences]
日期:2022-01-01
卷期号:27 (6): 3375-3375
被引量:4
标识
DOI:10.3934/dcdsb.2021189
摘要
<p style='text-indent:20px;'>In this paper, we aim to investigate the dynamic transition of the Klausmeier-Gray-Scott (KGS) model in a rectangular domain or a square domain. Our research tool is the dynamic transition theory for the dissipative system. Firstly, we verify the principle of exchange of stability (PES) by analyzing the spectrum of the linear part of the model. Secondly, by utilizing the method of center manifold reduction, we show that the model undergoes a continuous transition or a jump transition. For the model in a rectangular domain, we discuss the transitions of the model from a real simple eigenvalue and a pair of simple complex eigenvalues. our results imply that the model bifurcates to exactly two new steady state solutions or a periodic solution, whose stability is determined by a non-dimensional coefficient. For the model in a square domain, we only focus on the transition from a real eigenvalue with algebraic multiplicity 2. The result shows that the model may bifurcate to an <inline-formula><tex-math id="M1">\begin{document}$ S^{1} $\end{document}</tex-math></inline-formula> attractor with 8 non-degenerate singular points. In addition, a saddle-node bifurcation is also possible. At the end of the article, some numerical results are performed to illustrate our conclusions.</p>
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