System Identification

Example: Two-dimensional reaction-diffusion system

The system identification tool is applied to a two-dimensional reaction-diffusion system in order to filter the data and to estimate model parameters. This system has a rich spatiotemporal dynamical behavior. If excited, the underlying chemical system produces concentration differences propagating through the chemical reactor. Target and spiral patterns are observed as well as spiral defect chaos. The underlying complex chemical reaction is simplified to a system of two variables, an activator v₁ and an inhibitor v₂.

Noisy observation (left) and the estimated pattern v₁ and v₂.

Estimated parameter for a model describing the reaction-diffusion system for different initial guesses. The true parameter is λ=1.

Reference:

Sitz, A., Kurths, J., Voss, H. U.: Identification of nonlinear spatiotemporal systems via partitioned filtering, Phys. Rev. E, 68, 2003, 016202, doi:10.1103/PhysRevE.68.016202, Article (PDF).