Unstable Invariant Manifolds in a Control Problem of the Combustion Process of a Gas Mixture

We consider a control problem of the combustion process of a gas mixture with taking into account the consumption of the reagent and oxidizer. In the system, depending on the values of the control parameter, either slow burnout regime or thermal explosion can be observed. It is shown that there is a critical regime separating these two regimes. The value of the control parameter corresponding to the critical regime is found. The analysis is based on the technique of the continuation of unstable invariant manifolds.