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This chapter is concerned with bifurcation theory, that roughly consists in the study of the topological changes of the solutions of some equations as some parameters are varying. Along this chapter we shall mainly focus on bifurcation arising when a simple eigenvalue crosses zero, typically yielding the appearance (or the disappearance) of branches of solutions. The results presented below are mostly based on the implicit function theorem, recalled in Section 3.1.

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Bifurcations

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  • 发表日期：

    2026年

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  • Arnaud Ducrot,
  • Quentin Griette,
  • Zhihua Liu,
  • Pierre Magal

摘要

This chapter is concerned with bifurcation theory, that roughly consists in the study of the topological changes of the solutions of some equations as some parameters are varying. Along this chapter we shall mainly focus on bifurcation arising when a simple eigenvalue crosses zero, typically yielding the appearance (or the disappearance) of branches of solutions. The results presented below are mostly based on the implicit function theorem, recalled in Section 3.1.