Local dynamics of an equation with two large different-order delays

Resumo

The behavior of solutions near an equilibrium of differential equations with two large different-order delays is studied. In critical cases, special equations (namely, quasi-normal forms) determining the dynamics of the original problem are constructed. As a rule, they have the form of nonlinear parabolic equations with two spatial variables. Asymptotic formulas are derived showing the relation between the solutions of a quasi-normal form and the original equation. The case of a small coefficient multiplying the term with a larger delay is studied separately.