The Role of Random Structures in Tissue Formation: From a Viewpoint of Morphogenesis in Stochastic Systems

Abstract

In this article, we investigate a type of biological tissue formation system with a random structure of reaction or/and diffusion, analyzing the connection with the results obtained in [Rajapakse & Smale, 2017a] for the corresponding deterministic systems and showing the major difference from these results. Interestingly, we find a dynamical phenomenon leading to morphogenesis or emergence in such a system. Also we find their transitions in this system, while only one type of dynamical behavior occurs for the deterministic systems that satisfy typical conditions. Using the stability theory of stochastic systems, we quantitatively elucidate how such a phenomenon is emergent in complex networks with random structures. We believe that our analytical results could be beneficial to understand the underlying mechanisms of complexity-induced functions in tissue formation within real environments.