Asymmetric Interaction of a Pair FitzHugh–Nagumo Oscillators

A pair of diffusion connected FitzHugh–Nagumo oscillators with an asymmetric interaction are considered. The problem is investigated in the close to critical case, where the matrix of the linear part of the system has a pair of purely imaginary eigenvalues. The normal form is constructed and its coefficients are determined depending on the initial parameters. The source system may be in two different situations: stable single-frequency oscillations with two different frequencies coexist or a single-frequency mode branches from the equilibrium. The obtained asymptotic results are supplemented by the numerical analysis.