On the interplay between intrinsic and extrinsic instabilities of spatially localized patterns
主 题: On the interplay between intrinsic and extrinsic instabilities of spatially localized patterns
报告人: Professor Yasumasa Nishiura (Tohoku University)
时 间: 2016-06-24 15:00-16:00
地 点: 理科一号楼 1114(数学所活动）
Spatially localized dissipative structures are observed in various fields, such as neural signaling, chemical reactions, discharge patterns, granular materials, vegetated landscapes and binary convection. These patterns are much simpler than single living cells, however they seem to inherit several characteristic “living state” features, such as self-replication, self-healing and robustness as a system. Flexible and adaptive switching of dynamics can also be observed when these structures collide with each other, or when they encounter environmental changes in the media. These behaviors stem from an interplay between the intrinsic instability of each localized pattern and the strength of external signals. To understand such an interplay, we explore the global geometric interrelation amongst all relevant solution branches of a corresponding system with approximate unfolding parameters. For instance, it has been uncovered that large deformation at strong collision is mapped into the network of unstable patterns called scattors, and that an organizing center for 1D pulse generators is a double homoclinic orbit of butterfly type. We will illustrate the impact of this approach by presenting its application in relation to the decision making process of amoeboid locomotion and hierarchical structures of ordered patterns arising in reaction diffusion systems and binary fluids.