Modelling of Critical Conditions for an Electrochemical Reactor Model

The paper deals with the critical phenomena in the dynamic model of an electrochemical reactor. We consider the case of an external resistance. We use asymptotic and geometrical approaches to obtain the conditions for the critical regime. The critical regime plays a bordering role between the slow processes and modes with self-acceleration. We show that the critical regime can be modelled by a canard. Asymptotic formulae for the canard and for the corresponding value of the control parameter of the system are obtained. The multidimensional invariant surface of variable stability (so-called black swan) is constructed. The black swan consists entirely of canards that model critical modes with various initial data. The black swan existence permits us to realize the critical regime with taking into account small perturbations in the chemical system.