Persistence of periodic patterns for perturbed biological oscillators

We apply the perturbation method and the Implicit Function Theorem to study the persistence of periodic patterns for two perturbed general biological oscillators: one weakly coupled ordinary differential equation and one reaction–diffusion system. The proof relies also on the formal adjoint equation theory and the Lyapunov–Schmidt method. For the perturbed reaction–diffusion model, spatial–temporal patterns such as rotating waves are shown to exist. Numerical simulations are presented to illustrate our analytical results.