[SS18] Qualitative analysis in mathematical biology

[SS18-01] Mass-conserving reaction-diffusion systems in biological pattern formations

*Yoshihisa Morita¹ (1. Ryukoku Joint Research Center for Science and Technology (Japan))

Keywords:

pattern formation,reaction-diffusion system,mass conservation,localized pattern,cell polarity,stability

A variety of spatial patterns and pattern dynamics are observed in many biological models. Among these models, reaction-diffusion systems are widely used to describe pattern formation. Despite their simple form, reaction-diffusion systems play a crucial role in understanding the mechanisms underlying phenomena in fields such as population biology, cell biology, and physiology. In this talk, I focus on the emergence of localized patterns in mass-conserving reaction-diffusion models describing cell polarity and introduce some mathematical contributions to their stability analysis, based on the works of Morita-Sakamoto (2020), Morita--Seirin-Lee (2021), and Morita-Oshita (2024).