Integral manifolds, canard-trajectories and thermal explosion (Q2761497)

Consider the singularly perturbed non-autonomous system NEWLINE\[NEWLINEy'=Y(x,y,z,a,\varepsilon),\quad \varepsilon z'=2xy+Z(x,y,z,a,\varepsilon),\tag{*}NEWLINE\]NEWLINE where \(y\) and \(z\) are scalars, \(\varepsilon\) is a positive small parameter, \(a\) is a scalar control parameter. The author gives conditions on \(Y\) and \(Z\) such that to any sufficiently small \(\varepsilon\) there is \(a=a(\varepsilon)\) such that (*) has a bounded global canard trajectory. This result is applied to a system modeling thermal explosion.