We study a slow-fast system with two slow and one fast variables. We assume that the slow manifold of the system possesses a fold and there is an equilibrium of the system in a small neighborhood of the fold. We derive a normal form for the system in a neighborhood of the pair “equilibrium-fold” and study the dynamics of the normal form. In particular, as the ratio of two time scales tends to zero we obtain an asymptotic formula for the Poincaré map and calculate the parameter values for the first period-doubling bifurcation. The theory is applied to a generalization of the FitzHugh – Nagumo system.

中文翻译：

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折叠慢流形附近具有平衡的慢-快系统

我们研究一个具有两个慢变量和一个快变量的慢快系统。 我们假设系统的慢流形具有折叠，并且在折叠的小邻域内存在系统平衡。我们推导出系统的范式 在“平衡折叠”对的邻域中 并研究范式的动力学。特别是，当两个时间尺度的比率趋于零时，我们得到庞加莱图的渐近公式 并计算第一个倍周期分岔的参数值。该理论被应用于 FitzHugh – Nagumo 系统的推广。