Qualitative analysis of a singularly-perturbed system of differential equations related to the van der Pol equations (Q1382719)

Consider the singularly perturbed system \((*)\) \(\varepsilon dx/dt = y-xz+\varepsilon e_1 (t)\), \(\varepsilon dz/dt = x^2 /3 - 1-z + \varepsilon e_3 (t)\), \(dy/dt =-x + e_2 (t)\) with \(0 < \varepsilon \ll 1, e_i (t)\) are bounded functions, \(i=1,2,3, e_2 (t)\) is small. By means of the attracting parts of the slow manifold \(S: =\{(x,y,z) \in \mathbb{R}^3\), \(y=xz\), \(z=x^2 / 3-1 \}\) of \((*)\) the author constructs a tube trapping solution to \((*)\) for sufficiently small \(\varepsilon\). In case \(e_i (t) \equiv 0\) for \(i=1,2,3\), the existence of at least one stable periodic solution can be proven. The author applies the result to the Oregonator as a model of the Belousov-Zhabitinskii reaction.