[Development of stationary dissipative structures in a unidimensional Turing--Prigogine model]

Area of Science:

• Theoretical chemistry
• Mathematical modeling
• Non-equilibrium thermodynamics

Context:

• Turing--Prigogine models describe pattern formation in chemical and biological systems.
• Stationary dissipative structures arise from non-equilibrium processes.
• Boundary conditions can influence system behavior.

Purpose:

• Derive an approximate formula for the critical parameter governing dissipative structure formation.
• Analyze the influence of domain length on pattern emergence.
• Quantify the negligible effect of boundary conditions in large systems.

Summary:

• An approximate formula for the critical parameter in the Turing--Prigogine linear model is derived.
• The formula is valid for sufficiently large spatial domains.
• An estimation demonstrates that boundary condition effects become negligible in the center of large segments.

Impact:

• Provides a tool for predicting pattern formation in large-scale systems.
• Simplifies analysis by defining conditions where boundary effects can be ignored.
• Contributes to understanding self-organization in complex systems.