Small-scale structure of nonlinearly interacting species advected by chaotic flows

We study the spatial patterns formed by interacting biological populations or reacting chemicals under the influence of chaotic
flows. Multiple species and nonlinear interactions are explicitly considered, as well as cases of smooth and nonsmooth forcing
sources. The small-scale structure can be obtained in terms of characteristic Lyapunov exponents of the flow and of the chemical
dynamics. Different kinds of morphological transitions are identified. Numerical results from a three-component plankton dynamics model support the theory, and they serve also to
illustrate the influence of asymmetric couplings.