5 papers
How Much Spatial Control Is Enough? Subdomain Optimal Control of Reaction-Diffusion Systems in Synthetic Developmental Biology
Mohamed Amine Ouchdiri, Hamza Faquir, Saad Benjelloun +1
Reaction--diffusion systems can produce spatial patterns such as stripes and spots by diffusion-driven instability. In synthetic developmental biology, such patterns are engineered…
Certified Reachable Sets for Nonlinear Reaction--Diffusion Systems
Mohamed Amine Ouchdiri, Mohamed Maghenem, Saad Benjelloun +1
Reachability analysis for dynamical systems seeks to compute a set containing all reachable states at a given time. Compared to ordinary differential equations (ODEs), the analysis…
Stabilization of the -D and -D Heat Equation via Modal Decomposition
Mohamed Amine Ouchdiri, Mohamed-Camil Belhadjoudja, Mohamed Maghenem +2
Modal decomposition has been used recently to achieve boundary stabilization of linear parabolic equations in the norm, in two and three dimensions. In one dimension, e…
Turing Patterns in a Morphogenetic Model with Single Regulatory Function
Mohamed Amine Ouchdiri, Saad Benjelloun, Adnane Saoud +1
Confirming Turing's theory of morphogens in developmental processes is challenging, and synthetic biology has opened new avenues for testing Turing's predictions. Synthetic mammali…
An optimal-control framework for reaction diffusion systems with application to synthetic developmental biology
Mohamed Amine Ouchdiri, Hamza Faquir, Saad Benjelloun +3
Reaction-diffusion systems offer a powerful framework for understanding self-organized patterns in biological systems, yet controlling these patterns remains a significant challeng…