Blue sky catastrophe in relaxation systems with one fast and two slow variables
The authors consider the three-dimensional relaxation system \(\dot{x}=f(x,y,\mu )\), \(\varepsilon \dot{y}=g(x,y)\), \(x=(x_1,x_2)\in\mathbb R^2\), \(y\in\mathbb R\). Here \(0<\varepsilon \ll 1\), \(|\mu |\ll 1\), \(f,g\in C^\infty\). Under a number of standard conditions described in [\textit{E. F. Mishchenko} and \textit{N. Kh. Rozov}, Differential equations with a small parameter and relaxation oscillations. Moskva: Nauka (1975; Zbl 0850.34001)], a blue sky catastrophe can take place in the described system providing the existence of classical relaxation oscillations.
scientific article; zbMATH DE number 5659337