Complex Patterns in a Simple System

Complex Patterns in a Simple System

November 26, 2024 | John E. Pearson
The article by John E. Pearson explores the complex spatio-temporal patterns that emerge in a simple reaction-diffusion model, specifically a variant of the Selkov model of glycolysis. These patterns, observed in numerical simulations, are in response to finite-amplitude perturbations and exhibit a variety of behaviors, including steady irregular patterns, spots that grow and divide, and chaotic spatio-temporal dynamics. The patterns range from regular hexagons to irregular steady states and chaotic patterns, with no stable Turing patterns observed due to the equal diffusion coefficients used. The study highlights the importance of non-uniform diffusion in promoting pattern formation and suggests biological relevance, particularly in the context of glycolysis. The author also discusses the implications of these findings for understanding pattern formation in various natural and artificial systems.The article by John E. Pearson explores the complex spatio-temporal patterns that emerge in a simple reaction-diffusion model, specifically a variant of the Selkov model of glycolysis. These patterns, observed in numerical simulations, are in response to finite-amplitude perturbations and exhibit a variety of behaviors, including steady irregular patterns, spots that grow and divide, and chaotic spatio-temporal dynamics. The patterns range from regular hexagons to irregular steady states and chaotic patterns, with no stable Turing patterns observed due to the equal diffusion coefficients used. The study highlights the importance of non-uniform diffusion in promoting pattern formation and suggests biological relevance, particularly in the context of glycolysis. The author also discusses the implications of these findings for understanding pattern formation in various natural and artificial systems.
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