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Effects of square spatial periodic forcing on oscillatory hexagon patterns in coupled reaction-diffusion systems
Weili Fan1, Fengna Ma1, Yuan Tong1
1College of Physics Science and Technology, Hebei University, Baoding 071002, People's Republic of China. fanweili@hbu.edu.cn.
Physical Chemistry Chemical Physics : PCCP
|September 23, 2023
Summary
External forcing impacts complex patterns in coupled reaction-diffusion systems. Indirect forcing can create resonant patterns, while direct forcing yields only non-resonant ones, offering control insights.
Area of Science:
- Complex systems dynamics
- Nonlinear pattern formation
- Chemical kinetics and diffusion
Background:
- Understanding pattern formation response to external stimuli is crucial, especially in systems with multiple interacting instabilities.
- Previous research focused on single instability systems, leaving complex patterns from multiple instabilities less explored.
- Reaction-diffusion systems are fundamental models for pattern formation in various scientific fields.
Purpose of the Study:
- To investigate the effects of square spatial periodic forcing on oscillatory hexagon patterns in a two-layer coupled reaction-diffusion system.
- To analyze the distinct responses of these patterns to direct and indirect additive forcing.
- To explore how forcing wavenumber and strength influence pattern transitions and characteristics.
Main Methods:
- Utilized a two-layer coupled reaction-diffusion model exhibiting both Turing and Hopf instabilities.
- Applied square spatial periodic forcing, differentiating between direct and indirect forcing methods.
- Analyzed the resulting spatio-temporal patterns by varying forcing parameters like wavenumber and strength.
Main Results:
- The system's response to spatial forcing varied significantly based on the forcing type (direct vs. indirect).
- Indirect forcing induced transitions to other oscillatory Turing patterns or resonant Turing patterns.
- Direct forcing exclusively resulted in non-resonant Turing patterns, irrespective of forcing parameters.
Conclusions:
- Spatial periodic forcing can effectively modify and control complex spatio-temporal patterns in multilayered systems.
- The type of forcing (direct or indirect) dictates the nature of the emergent patterns, offering tunable control.
- Findings provide valuable insights for applications in biological and ecological pattern formation and control.
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