Slow integral manifolds with stability change in the case of a fast vector variable
Consider the singularly perturbed system \[ dx/dt =X(x,y,t,\varepsilon), \] \[ \varepsilon dy_1/dt =2ty_1+a(y,\varepsilon)+Z_1(x,y_1,y_2,t,\varepsilon), \] \[ \varepsilon dy_2/dt = A(t)y_2 + B a(y,\varepsilon) + Z_2(x,y_1,y_2,t,\varepsilon) , \] with \(x \in \mathbb{R}^n\), \(z_1 \in \mathbb{R}\), \(z_2 \in \mathbb{R}^m\), \(0<\varepsilon \ll 1\). The author derives conditions on the matrix \(A \) and the functions \(X, Z_1, Z_2 \) ensuring the existence of a function \(a(x,\varepsilon)\) such that the system has a slow integral manifold \( y=h(x,t,\varepsilon)\) with a change of attractivity. As an example, some model from physical chemistry is considered.
scientific article; zbMATH DE number 1916193