Integral manifolds, canards and black swans

Applying canards for modelling critical regimes promoted to solve some interesting and important problems of combustion theory. Moreover, the analysis of these problems involves the necessity of proofs of new theorems of differential equations. The existence and properties of integral manifolds of variable stability for ordinary differential equations without singular perturbations and some applications were considered. It is noted that very interesting applications of canards in models of economics and chemical kinetics were obtained.