Some results on the existence of weak periodic solutions for quasilinear parabolic systems with L1 data

The aim of this paper is to prove the existence of weak periodic solution and super solution for M×M reaction diffusion system with L1 data and nonlinearity on the gradient. The existence is proved by the technique of sub and super solution and Schauder fixed point theorem.

On a numerical bifurcation analysis of a particle reaction-diffusion model for a motion of two self-propelled disks

Theoretical analysis using mathematical models is often used to understand a mechanism of collective motion in a self-propelled system. In the experimental system using camphor disks, several kinds of characteristic motions have been observed due to the interaction of two camphor disks. In this paper, we understand the emergence mechanism of the motions caused by the interaction of two self-propelled bodies by analyzing the global bifurcation structure using the numerical bifurcation method for a mathematical model. Finally, it is also shown that the irregular motion, which is one of the characteristic motions, is chaotic motion and that it arises from periodic bifurcation phenomena and quasi-periodic motions due to torus bifurcation.