Invariant sets and attractors for Hanusse-type chemical systems with diffusions

We are concerned with Hanusse-type chemical models with diffusions. We show that some bounded invariant sets ⊂RN found for the ODE Hanusse-type models (corresponding to the case when diffusions are neglected) can be used to define invariant sets ⊂L∞(Ω)N with respect to the corresponding Hanusse-type PDE models (involving diffusions), where Ω⊂Rn, n≤3, denotes the reaction domain. Simulations for both the ODE and PDE Hanusse-type models are performed for suitable coefficients of the polynomials representing the reaction terms, showing that the attractors for the ODE model are also attractors, in fact the only attractors, for the PDE model.