The stability and the two-parameter bifurcation of a two-dimensional discrete Gierer–Meinhardt system are investigated in this paper. The analysis is carried out both theoretically and numerically. It is found that the model can exhibit codimension-two bifurcations ([Formula: see text], [Formula: see text], and [Formula: see text] strong resonances) for certain critical values at the positive fixed point. The normal forms are obtained by using a series of affine transformations and bifurcation theory. Numerical simulations including bifurcation diagrams, phase portraits and basins of attraction are conducted to validate the theoretical predictions, which can also display some interesting and complex dynamical behaviors.

中文翻译：

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离散Gierer-Meinhardt系统的余维-二分岔分析

本文研究了二维离散Gierer-Meinhardt系统的稳定性和两参数分岔。分析是在理论上和数值上进行的。发现对于正不动点的某些临界值，该模型可以表现出余维-两个分岔（[公式：见文]、[公式：见文]和[公式：见文]强共振）。范式是通过一系列仿射变换和分岔理论得到的。进行了包括分岔图、相图和吸引力盆地在内的数值模拟来验证理论预测，这也可以显示一些有趣和复杂的动力学行为。