Spatiotemporal patterns in coupled reaction-diffusion systems with nonidentical kinetics

Area of Science:

• Nonlinear Science
• Complex Systems
• Pattern Formation

Background:

• Nonequilibrium systems often comprise multiple interacting layers or units.
• Understanding coupling interactions is fundamental to nonlinear science.

Purpose of the Study:

• To investigate spatio-temporal pattern formation in a nonlinearly coupled two-layer Turing system.
• To analyze the role of Turing mode type and coupling form on pattern dynamics.

Main Methods:

• Simulation of a two-layer Turing system with nonidentical reaction kinetics.
• Investigation of supercritical-subcritical and supercritical-supercritical Turing mode interactions.
• Analysis of linear versus nonlinear coupling effects on pattern formation.

Main Results:

• Spontaneous formation of stationary resonant superlattice patterns in both interaction types.
• Emergence of dynamic patterns in the supercritical-supercritical case, potentially due to destabilized spike solutions.
• Nonlinear coupling increases pattern complexity and relaxes spatial resonance conditions.

Conclusions:

• The type of Turing mode interaction and coupling significantly influence pattern formation and selection.
• Nonlinear coupling offers advantages over linear coupling in pattern generation and resonance requirements.
• Simulation results align with experimental observations in dielectric barrier discharge systems.