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Nonlinear dynamics and spatiotemporal patterns of a delayed reaction-diffusion system on a square domain.
Daifeng Duan1, Yaqi Chen2, Dongming Jia1
1Nanjing University of Posts and Telecommunications, College of Science, Nanjing 210023, People's Republic of China.
Physical Review. E
|February 20, 2026
Summary
This study analyzes pattern formation in delayed reaction-diffusion systems, revealing symmetry-breaking dynamics like rotating waves. The research provides a predictive framework linking model parameters to nonlinear pattern selection and stability.
Area of Science:
- Mathematical modeling
- Theoretical physics
- Chemical kinetics
Background:
- Reaction-diffusion systems are fundamental to understanding pattern formation in nature.
- Delayed systems introduce complex dynamics, including oscillations and waves.
- Spatotemporal pattern selection is a key challenge in nonlinear dynamics.
Purpose of the Study:
- To analyze pattern formation in delayed reaction-diffusion systems on a square domain.
- To reveal symmetry-breaking dynamics near criticality.
- To develop a predictive approach for nonlinear pattern selection and stability.
Main Methods:
- Bifurcation theory
- Amplitude equations
- Normal form derivation
- Application to Ginzburg-Landau and predator-prey models
Main Results:
- Symmetry-breaking dynamics identified, including rotating waves and quasiperiodic solutions.
- Explicit normal forms derived for systems with spatial symmetry.
- Framework developed to predict pattern selection and stability based on model parameters.
- Explanation of spatiotemporal patterns like standing and spiral waves.
Conclusions:
- The study provides a robust framework for analyzing pattern formation in delayed reaction-diffusion systems.
- The predictive approach facilitates understanding and controlling complex nonlinear patterns.
- The findings have implications for diverse fields utilizing reaction-diffusion models.
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