Monte Carlo simulation and linear stability analysis of Turing pattern formation in reaction-subdiffusion systems.

Area of Science:

• Computational physics
• Chemical kinetics
• Non-equilibrium systems

Background:

• Subdiffusion is prevalent in complex systems but lacks efficient numerical simulation methods, especially when reactions are involved.
• Studying reaction-subdiffusion dynamics is crucial for understanding pattern formation in various scientific domains.

Purpose of the Study:

• To develop an efficient Monte Carlo algorithm for simulating reaction-subdiffusion systems.
• To investigate the impact of subdiffusion on Turing pattern formation within the Schnakenberg model.

Main Methods:

• Development of a novel Monte Carlo algorithm integrating the Gillespie algorithm and continuous-time random walk.
• Simulation of the Schnakenberg model under varying degrees of subdiffusion and particle numbers.
• Linear stability analysis to corroborate simulation results.

Main Results:

• Increased subdiffusion makes destabilizing the homogeneous state and forming Turing patterns more difficult.
• Lower particle numbers lead to increased fluctuations, further inhibiting Turing pattern formation.
• A higher ratio of diffusion constants is required to observe Turing patterns as subdiffusion increases.

Conclusions:

• The developed algorithm provides an efficient tool for studying reaction-subdiffusion systems.
• Subdiffusion significantly influences the conditions necessary for Turing pattern emergence.
• The findings offer insights into pattern formation dynamics in systems with anomalous diffusion.