Turing-Hopf Bifurcation Analysis of the Sel'kov-Schnakenberg System
Turing-Hopf Bifurcation Analysis of the Sel'kov-Schnakenberg System
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DOI：
10.1142/s0218127423500128
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发表时间：
2023-01
期刊：
影响因子：
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通讯作者：
Yuying Liu;Xin Wei
中科院分区：
文献类型：
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作者：
Yuying Liu;Xin Wei
本文研究了Sel'kov-Schnakenberg系统的时空动力学。利用线性稳定性理论研究了正定常平衡态的稳定性。通过改变模型中的两个参数，可以产生Hopf分支和Turing-Hopf分支。计算了系统在Turing-Hopf奇异点附近的规范形，探讨了系统的复杂动力学行为。最后，通过数值仿真验证了理论分析的正确性.结果表明，Sel'kov-Schnakenberg系统在Turing-Hopf奇点附近具有复杂的动力学行为，包括非齐次定态、齐次周期解和非齐次周期解的存在性.
In this paper, we investigate the spatiotemporal dynamics of the Sel’kov–Schnakenberg system. The stability of the positive constant steady state is studied by the linear stability theory. Hopf bifurcation and Turing–Hopf bifurcation are generated by varying two parameters in the model. The normal form near the Turing–Hopf singularity is calculated to explore the complex dynamics of the system. Finally, numerical simulations are carried out to verify the theoretical results. Our results show that the Sel’kov–Schnakenberg system exhibits complex dynamics near the Turing–Hopf singularity, including the existence of inhomogeneous steady states, homogeneous periodic solutions and inhomogeneous periodic solutions.