Speaker
Description
Reaction-diffusion-ODE systems have emerged as powerful models for pattern formation in developmental biology, capturing the interplay between diffusive and non-diffusive nonlinear processes. These systems exhibit a rich variety of spatial structures, including classical Turing patterns and far-from-equilibrium patterns. Previous studies focused on diffusion-driven instability (DDI) generated by instability of the purely non-diffusive subsystem, which destabilizes classical Turing patterns. In contrast, we show that DDI can also arise from subsystems coupling non-diffusive and slowly diffusing components, giving rise to dynamics involving three distinct spatial scales. Further, we characterize conditions for the emergence of stable Turing patterns via bifurcation theory in a three-equation system and prove the existence of far-from-equilibrium patterns in general reaction-diffusion-ODE frameworks. As illustrative examples, we apply our results to specific models, demonstrating the broad applicability of the approach.
