TY - JOUR
T1 - Dynamics of traveling pulses in heterogeneous media of jump type
AU - Nishiura, Yasumasa
AU - Oyama, Yoshihito
AU - Ueda, Kei Ichi
PY - 2007
Y1 - 2007
N2 - We study pulse dynamics in one-dimensional heterogeneous media. In particular we focus on the case where the pulse is close to the singularity of codim 2 type consisting of drift and saddle-node instabilities in a parameter space. We assume that the heterogeneity is of jump type, namely one of the coefficients of the system undergoes an abrupt change at one point in the space. Depending on the height of this jump, the responses of pulse behavior are penetration, splitting, and rebound. Taking advantage of the fact that pulse is close to the singularity, the PDE dynamics can be reduced to a finite-dimensional system, which displays the three behaviors. Moreover it takes a universal form independent of model systems, and is valid for much more general heterogeneities such as bump, periodic, and random cases.
AB - We study pulse dynamics in one-dimensional heterogeneous media. In particular we focus on the case where the pulse is close to the singularity of codim 2 type consisting of drift and saddle-node instabilities in a parameter space. We assume that the heterogeneity is of jump type, namely one of the coefficients of the system undergoes an abrupt change at one point in the space. Depending on the height of this jump, the responses of pulse behavior are penetration, splitting, and rebound. Taking advantage of the fact that pulse is close to the singularity, the PDE dynamics can be reduced to a finite-dimensional system, which displays the three behaviors. Moreover it takes a universal form independent of model systems, and is valid for much more general heterogeneities such as bump, periodic, and random cases.
KW - Bifurcation (35B32)
KW - Homoclinic and heteroclinic solutions (34C37)
KW - Reaction-diffusion equations (35K57)
UR - http://www.scopus.com/inward/record.url?scp=85009197482&partnerID=8YFLogxK
U2 - 10.14492/hokmj/1285766659
DO - 10.14492/hokmj/1285766659
M3 - 学術論文
AN - SCOPUS:85009197482
SN - 0385-4035
VL - 36
SP - 207
EP - 242
JO - Hokkaido Mathematical Journal
JF - Hokkaido Mathematical Journal
IS - 1
ER -