Speaker
Description
Reaction–diffusion–ODE systems arise in models of biological pattern formation, for example in symmetry breaking during regeneration in Hydra. These systems couple diffusive and non-diffusive nonlinear processes. In contrast to classical reaction–diffusion systems, such models may exhibit patterns with singularities, including jump discontinuities, which complicate the analysis of nonlinear stability. In this work, we develop a general framework for the stability analysis of steady states by establishing conditions for nonlinear stability and instability of bounded stationary solutions in reaction–diffusion–ODE systems. As an application, we derive conditions for diffusion-driven instability (DDI), a key mechanism underlying the emergence of Turing patterns in these systems. Finally, we illustrate the results with numerical simulations of example models.
