Easun Arunachalam Rose Hills
Stability maintenance in reaction-diffusion systems
Interplay between spatial organization and interconversion of different molecules leads to complex pattern formation in simple chemical systems. Some have suggested implications for biological systems, especially in the context of embryonic development. However, unlike idealized chemical systems, biological systems are characterized by complex and dynamic environments. Nevertheless, biological pattern formation appears to be largely stable. This stands in stark contrast to current theories, which predict extreme sensitivity to fluctuations and initial conditions in systems with feedback delays – delays in the response of a system to a stimulus. A comprehensive theory must account for stability despite such time delays, which are common in biological systems. My goal is to develop a theoretical description of pattern formation in the presence of perturbations. Using theory and computer simulation, I will contribute to a quantitative description of stability maintenance in the face of feedback delays. A mathematical description of such systems is valuable because it provides insights into how to manipulate their behavior. It is especially critical to understanding and preventing birth defects, and for developing advanced manufacturing techniques.