Mechanism of spatiotemporal patterns generated by reaction-diffusion systems

这项研究涉及模拟生物现象中图案形成的反应-扩散系统的动力学。我考虑了反应扩散系统中参数对其动力学的作用。对于激活-抑制系统，“模式崩溃”的机制是可以理解的。我们还考虑了一维趋化方程来研究解的渐近行为，以及三组分的反应扩散方程来证明空间模式的存在性和稳定性。

This study is concerned with the dynamics of reaction-diffusion systems modeling pattern formation in biological phenomena. I considered the role of parameters in reaction-diffusion systems on its dynamics. Concerning an activator-inhibitor system, the mechanism of "collapse of patterns" could be understood. I also considered one-dimensional chemotaxis equations to study the asymptotic behavior of solutions, and three component reaction-diffusion equations to show the existence and stability of spatial patterns.