Numerical simulation and analysis of complex patterns in a two-layer coupled reaction diffusion system

• Published in: Chinese physics B Vol. 24; no. 4; pp. 491 - 496
• Main Author: 李新政 白占国 李燕 贺亚峰 赵昆
• Format: Journal Article
• Language: English
• Published: 01.04.2015
• Subjects: Dynamical systems; Hexagons; Instability; Joining; Mathematical models; Nonlinear dynamics; Stability; Wavelengths; 共振相互作用; 反应扩散系统; 图案; 数值模拟; 耦合强度; 耦合模型; 长波长; 非线性系统
• ISSN: 1674-1056; 2058-3834; 1741-4199
• DOI: 10.1088/1674-1056/24/4/048201

The resonance interaction between two modes is investigated using a two-layer coupled Brusselator model. When two different wavelength modes satisfy resonance conditions, new modes will appear, and a variety of superlattice patterns can be obtained in a short wavelength mode subsystem. We find that even though the wavenumbers of two Turing modes are fixed, the parameter changes have influences on wave intensity and pattern selection. When a hexagon pattern occurs in the short wavelength mode layer and a stripe pattern appears in the long wavelength mode layer, the Hopf instability may happen in a nonlinearly coupled model, and twinkling-eye hexagon and travelling hexagon patterns will be obtained. The symmetries of patterns resulting from the coupled modes may be different from those of their parents, such as the cluster hexagon pattern and square pattern. With the increase of perturbation and coupling intensity, the nonlinear system will con- vert between a static pattern and a dynamic pattern when the Turing instability and Hopf instability happen in the nonlinear system. Besides the wavenumber ratio and intensity ratio of the two different wavelength Turing modes, perturbation and coupling intensity play an important role in the pattern formation and selection. According to the simulation results, we find that two modes with different symmetries can also be in the spatial resonance under certain conditions, and complex patterns appear in the two-layer coupled reaction diffusion systems.