TY - JOUR
T1 - Stability of steady-state solutions to a prey-predator system with cross-diffusion
AU - Kuto, Kousuke
N1 - Funding Information:
$This work was partially supported by JSPS Research Fellowships for Japanese Young Scientists (No. 05726). ·Corresponding author. Fax: +81-3-5286-3483. E-mail address: kuto@toki.waseda.jp.
PY - 2004/3/1
Y1 - 2004/3/1
N2 - This paper is concerned with a cross-diffusion system arising in a prey-predator population model. The main purpose is to discuss the stability analysis for coexistence steady-state solutions obtained by Kuto and Yamada (J. Differential Equations, to appear). We will give some criteria on the stability of these coexistence steady states. Furthermore, we show that the Hopf bifurcation phenomenon occurs on the steady-state solution branch under some conditions.
AB - This paper is concerned with a cross-diffusion system arising in a prey-predator population model. The main purpose is to discuss the stability analysis for coexistence steady-state solutions obtained by Kuto and Yamada (J. Differential Equations, to appear). We will give some criteria on the stability of these coexistence steady states. Furthermore, we show that the Hopf bifurcation phenomenon occurs on the steady-state solution branch under some conditions.
KW - Cross diffusion
KW - Hopf bifurcation
KW - Lyapunov-Schmidt reduction
KW - Stability
KW - Steady-state solution
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U2 - 10.1016/j.jde.2003.10.016
DO - 10.1016/j.jde.2003.10.016
M3 - Article
AN - SCOPUS:1342328537
SN - 0022-0396
VL - 197
SP - 293
EP - 314
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 2
ER -