New mathematics for understanding complex patterns in the natural sciences

本计画旨在借由发展及延伸数学技巧，探讨反应扩散方程式中基本二维模式（如斑点及条纹）的相互作用。这些基本的平面结构形成了更复杂模式的主干，例如，在描述神经轴突中脉冲传播和植被模式形成的模型中观察到。这项研究的未来影响将具有经济和环境效益。例如，该项目将加深对相互作用模式的理解，从而深入了解植被在正在经历荒漠化的生态系统中的作用。

This project aims to examine the interaction of fundamental two-dimensional patterns such as spots and stripes in reaction-diffusion equations, by developing and extending mathematical techniques. These fundamental planar structures form the backbone of more complex patterns and are, for example, observed in models that describe the propagation of impulses in nerve axons and the formation of vegetation patterns. The future impact of this research will have economic and environmental benefits. For example, the project will develop a deeper understanding of interacting patterns that will provide insights into the role of vegetation in ecosystems that are undergoing desertification.