In this paper, steady state bifurcations arising from the reaction–diffusion equations are investigated. Using the Lyapunov–Schmidt reduction on a square domain, a simple, and a double steady state bifurcation caused by the symmetry of spatial region is obtained. By examining the reduced bifurcation equations, complete bifurcation scenario and patterns at simple and double steady state bifurcation points are obtained. Numerical simulations support the theoretical results.

中文翻译：

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稳态分岔和反应模式-扩散方程

在本文中，研究了由反应扩散方程引起的稳态分岔。利用平方域上的Lyapunov-Schmidt约简，得到了由空间区域对称性引起的简单双稳态分岔。通过检查简化的分岔方程，获得了简单和双稳态分岔点处的完整分岔场景和模式。数值模拟支持理论结果。