Computation of inertial manifolds in biological models. FitzHugh–Nagumo model

Inertial manifolds are related to the large time behaviour of dynamical systems. An algorithm, based on the Lyapunov–Perron method, is implemented here and used to construct a sequence of approximate inertial manifolds for a biological model. The hypotheses of the Jolly, Rosa, Temam's algorithm are verified for the FitzHugh–Nagumo model in the case of real eigenvalues. This algorithm is used for the construction of approximate inertial manifolds.