The Bifurcation Growth Rate for the Robust Pattern Formation in the Reaction–Diffusion System on the Growing Domain
Year: 2025
Type: article
Abstract: This study investigates the maintenance and disappearance of patterns as an initial state, which are initially formed on a static domain, in a reaction–diffusion system on a time-dependent growing domain, building on our previous model for pattern transitions in organisms like Pelodiscus sinensis. While earlier work focused on pattern disappearance, we now explore conditions under which patterns are sustained as the domain grows. By simplifying a non-autonomous system with time-dependently decaying diffusion and reaction terms, we analytically identify bifurcation points where formed patterns either persist or fade away. We apply the Gray–Scott (GS) model to the reaction term and a Turing pattern to an initial state, and demonstrate that the Turing mechanism is useful for analytically identifying the bifurcation point even on a growing domain. Numerical simulations confirm that patterns can be maintained or disappear depending on the growth rate’s relationship with a theoretically derived bifurcation point. Our results highlight the potential to control a formed pattern maintenance in growing domains with a simplified, adjustable model based on a single parameter, the growth rate, potentially providing a new step in exploring the possibility of applying the model to biomimetics and other fields.
Authors: Shin Nishihara, Toru Ohira
Institution: Nagoya University
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4413609828