Assistant Professor Kei Nishi

Area and Subject Taught Applied Analysis
Research Theme(s) Dynamics of localized patterns in reaction-diffusion systems
Academic Degrees Doctor (Mathematics), Hokkaido University
Keywords for Research Field Pattern formation, Reaction-diffusion systems, Bifurcation theory
Office Phone Number Not Public
e-mail E-mail

Research Overview

Localized patterns are ubiquitously observed in many dissipative systems. Especially, reaction-diffusion systems admit spatially localized patterns such as a pulse or a spot which exhibits spontaneous traveling, oscillatory, and even chaotic motions. My interest is in revealing the underlying mechanism for the dynamics of such localized solutions from a viewpoint of dynamical system theory.
Over the past decades, analytical techniques such as the Evans function and (geometric) singular perturbation methods have been developed to investigate the existence and stability of a single localized pattern, especially for a traveling pulse solution arising in one-dimensional space. On the other hand, the situations where such a localized pattern interacts with other localized patterns or a defect in the medium are also commonplace in nature, giving rise to a wide variety of collective motions and defect-mediated dynamics. However, the interaction among the many localized patterns leads to the appearance of many kinds of transient pattern, making the problem hard to treat analytically, and hence much remains to be elucidated. I address these tough, yet challenging problems by means of numerical simulations as well as analytical methods such as singular perturbation and center manifold reduction.

Notable Publications and Works in the Last Three Years

  1. S.-I. Ei, K. Nishi, Y. Nishiura, and T. Teramoto: Annihilation of two interfaces in a hybrid system, Discrete and Continuous Dynamical Systems - Series S, 8 (2015), 857–869.
  2. Kei Nishi, Ken Wakai, Tomoaki Ueda, Miyu Yoshii, Yumihiko S. Ikura, Hiraku Nishimori, Satoshi Nakata, and Masaharu Nagayama, Bifurcation phenomena of two camphor disks on an annular field depending on system length, Physical Review E, 92 (2015), 022910-1-10.
  3. K. Nishi, Y. Nishiura, and T. Teramoto: Dynamics of two interfaces in a hybrid system with jump-type heterogeneity, Japan Journal of Industrial and Applied Mathematics, 30 (2013), 351-395.
  4. K. Nishi, Y. Nishiura, and T. Teramoto: Behaviors of a front-back pulse arising in a bistable medium with jump-type heterogeneity, Advanced Studies in Pure Mathematics, 64 (2015), 479-487.