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Stability and Hopf Bifurcation in the General Langford System

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Abstract

This paper is concerned with the general Langford system under homogeneous Neumann boundary conditions. The stabilities of constant solutions are discussed for the general Langford ODE and PDE systems, respectively. Based on the stability results, for the Langford ODE system, the existence, bifurcation direction and stability of periodic solutions are established. Then for the Langford PDE system, by the center manifold theory and the normal form method, the direction of Hopf bifurcation and the stability of spatially homogeneous periodic solutions are investigated. Finally, numerical simulations are shown to support and supplement the results of theoretical analysis.

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Authors and Affiliations

  1. School of Mathematics and Data Science, Shaanxi University of Science and Technology, Xi’an, 710021, China

    Gaihui Guo, Jingjing Wang & Meihua Wei

Authors
  1. Gaihui Guo
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  2. Jingjing Wang
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  3. Meihua Wei
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Contributions

GG and MW contributed to the conception of the study and wrote the main manuscript text. JW prepared figures. All authors reviewed the manuscript.

Corresponding authors

Correspondence to Gaihui Guo or Meihua Wei.

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The work is supported by the National Natural Science Foundation of China (61872227, 12061081, 12126420).

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Guo, G., Wang, J. & Wei, M. Stability and Hopf Bifurcation in the General Langford System. Qual. Theory Dyn. Syst. 22, 144 (2023). https://doi.org/10.1007/s12346-023-00832-w

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