Multiple existence and stability of steady-states for a prey-predator system with cross-diffusion

Kousuke Kuto, and Yoshio Yamada. "Multiple existence and stability of steady-states for a prey-predator system with cross-diffusion." Banach Center Publications 66.1 (2004): 199-210. <http://eudml.org/doc/282103>.

@article{KousukeKuto2004,
abstract = {This article discusses a prey-predator system with cross-diffusion. We obtain multiple positive steady-state solutions of this system. More precisely, we prove that the set of positive steady-states possibly contains an S or ⊃-shaped branch with respect to a bifurcation parameter in the large cross-diffusion case. Next we give some criteria on the stability of these positive steady-states. Furthermore, we find the Hopf bifurcation point on the steady-state solution branch in a certain case. Our method of analysis uses the idea developed by Du and Lou [6] and is based on the bifurcation theory and the Lyapunov-Schmidt reduction technique.},
author = {Kousuke Kuto, Yoshio Yamada},
journal = {Banach Center Publications},
keywords = {cross-diffusion; steady-state; multiple existence; stability; Hopf bifurcation; Lyapunov-Schmidt reduction},
language = {eng},
number = {1},
pages = {199-210},
title = {Multiple existence and stability of steady-states for a prey-predator system with cross-diffusion},
url = {http://eudml.org/doc/282103},
volume = {66},
year = {2004},
}

TY - JOUR
AU - Kousuke Kuto
AU - Yoshio Yamada
TI - Multiple existence and stability of steady-states for a prey-predator system with cross-diffusion
JO - Banach Center Publications
PY - 2004
VL - 66
IS - 1
SP - 199
EP - 210
AB - This article discusses a prey-predator system with cross-diffusion. We obtain multiple positive steady-state solutions of this system. More precisely, we prove that the set of positive steady-states possibly contains an S or ⊃-shaped branch with respect to a bifurcation parameter in the large cross-diffusion case. Next we give some criteria on the stability of these positive steady-states. Furthermore, we find the Hopf bifurcation point on the steady-state solution branch in a certain case. Our method of analysis uses the idea developed by Du and Lou [6] and is based on the bifurcation theory and the Lyapunov-Schmidt reduction technique.
LA - eng
KW - cross-diffusion; steady-state; multiple existence; stability; Hopf bifurcation; Lyapunov-Schmidt reduction
UR - http://eudml.org/doc/282103
ER -