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Bifurcation diagrams and Turing patterns in a chemical self-replicating reaction-diffusion system with cross
Jessica M Chung1, Enrique Peacock-López
1Department of Chemistry, Williams College, Williamstown, Massachusetts 01267, USA.
The Journal of Chemical Physics
|November 13, 2007
Summary
This study models chemical self-replication, incorporating the square root rate law and cross-diffusion to analyze pattern formation. Generalized results provide exact relations for bifurcations in complex chemical systems.
Area of Science:
- Chemical kinetics
- Pattern formation
- Biophysical chemistry
Background:
- Oligonucleotide and helical peptide self-replication follows a square root rate law.
- Previous models focused on ideal replicators, lacking nonlinearities and enzymatic sinks.
Purpose of the Study:
- To generalize chemical self-replication models by including the square root rate law and nonlinearities.
- To investigate the role of cross-diffusion in pattern formation within these generalized models.
- To derive exact relations for bifurcations in complex chemical systems.
Main Methods:
- Extension of ideal replicator models to incorporate nonlinear kinetics and enzymatic sinks.
- Analysis of pattern formation using cross-diffusion terms.
- Derivation of general relations for Poincaré-Andronov-Hopf and Turing bifurcations.
Main Results:
- Exact general relations for Poincaré-Andronov-Hopf and Turing bifurcations were obtained.
- The generalized model encompasses Higgins, Autocatalator, and Templator models as specific cases.
- Cross-diffusion plays a significant role in pattern formation within the studied systems.
Conclusions:
- The generalized model provides a comprehensive framework for studying chemical self-replication with nonlinearities.
- The derived bifurcation relations offer insights into pattern formation mechanisms.
- This work advances the understanding of complex chemical systems and their dynamics.
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