Study on the strong interaction among spatially localized patterns in dissipative systems

自然界中普遍存在着空间局域化的运动模式，如神经系统、气体放电现象、化学反应、二元对流、真黏菌的运动等。它们通过与环境的碰撞或相互作用表现出各种动态模式，如湮灭、合并和分裂。为了更全面地理解这些现象，我们结合了几种理论和数值方法，如高维局部分叉分析、数值路径跟踪和降阶到有限维系统，这些方法使我们能够阐明控制这些动力学的数学机制。

Spatially localized traveling patterns appear ubiquitously in nature such as neural system, gas-discharge phenomena, chemical reaction, binary convection, and motion of true slime mold. They display a variety of dynamic patterns like annihilation, coalescence,and splitting via collisions or interaction with environments. For the comprehensive understanding of these phenomena, we combine several theoretical and numerical approaches like local bifurcation analysis of higher codimension, numerical path-tracking, and reduction to finite dimensional systems, which allow us to clarify the mathematical mechanism controlling behind those dynamics.