Major research activity
Nature produces many beautiful patterns in our surroundings, including periodicities, symmetries and rhythms. For instance, zebras have periodic black and white stripes, honeycombs have 120-degree rotational symmetry, and hearts beat with a cardiac rhythm. In the past few decades, systems of equations that were originally developed to describe the reaction and diffusion of chemical substances were found to also provide insights into the mechanisms behind such natural phenomena. Indeed, many numerical simulations carried out for certain reaction-diffusion systems have produced spatiotemporal patterns similar to those produced by nature. However, further analysis of such systems is still required in order to form a more complete understanding of the mechanisms behind many natural phenomena. In our laboratory, we have been engaged in studying these mechanisms by analyzing the corresponding reaction-diffusion systems. In particular, we have focused on phenomena involving advection, such as the formation of sunflower patterns by E. coli. and honeycomb patterns by honeybees. In such cases, advection is induced by chemotaxis, which involves movement towards chemoattractants. The reaction-diffusion system that describes these phenomena is referred to as a reaction-diffusion-chemotaxis system or simply a chemotaxis system. During the last decade, we have been involved in an analysis of such chemotaxis systems, and have derived solutions and clarified their dynamics, including the existence of attractors. We have also carried out bifurcation analyses of honeycomb patterns. In the future, we plan to extend our study of chemotaxis and other reaction-diffusion systems to gain insights into a range of natural phenomena.
Major relevant publications
- E. Nakaguchi and K. Osaki, L^p-Estimates of Solutions to n-Dimensional Parabolic-Parabolic System for Chemotaxis with Subquadratic Degradation, Funkcial. Ekvac., to appear.
- T. Narumi and K. Osaki, Three-Dimensional Pattern Formations in a Biological Model of Chemotaxis and Growth, RIMS Kokyuroku 1917 (Nov, 2014), 86-93.
- E. Nakaguchi and K. Osaki, Global Solutions and Exponential Attractors of a Parabolic-Parabolic System for Chemotaxis with Subquadratic Degradation, DCDS-B 18(10), 2627-2646 (2013).
- K. Kuto, K. Osaki, T. Sakurai and T. Tsujikawa, Spatial Pattern Formation in a Chemotaxis-Diffusion-Growth Model, Physica D241, 1629-1639, (2012).
- T. Okuda and K. Osaki, Bifurcation of Hexagonal Patterns in a Chemotaxis-Diffusion-Growth System, Nonlinear Anal. Real World Appl. 12, 3294-3305, (2011).