Characterization of spatiotemporal chaos in an inhomogeneous active media

We study a reaction diffusion system of the activator-inhibitor type with inhomogeneous reaction terms showing spatio-temporal chaos.
We characterize the topological properties of the unstable orbits in the slow chaotic dynamics appearing, which can be embedded in three dimensions. We perform a biorthogonal decomposition analyzing the minimum number of modes necessary to find the same organization of unstable orbits.