IJPAM: Volume 46, No. 4 (2008)

THE CROSS-DIFFUSION DRIVEN INSTABILITY IN
A SPRUCE BUDWORM-APHID INTERACTION MODEL

Shihua Zhu$^1$, Zhigui Lin$^2$, Jiahong Liu$^3$
$^{1,2,3}$School of Mathematical Science
Yangzhou University
Yangzhou, 225002, P.R. CHINA
$^2$e-mail: zglin68@hotmail.com


Abstract.In this paper the instability of the uniform equilibrium of a spruce budworm-aphid interaction model is discussed. In bounded domain and unbounded domain, the sufficient conditions for the instability are obtained respectively. We show that under certain conditions cross-diffusion can induce the instability of the uniform equilibrium, which is stable for the kinetic system and for the self-diffusion reaction system, on the other hand, cross-diffusion can also stabilize the uniform equilibrium, which is stable for the kinetic system but unstable for the self-diffusion reaction system. Numerical simulations are presented to illustrate the main results.

Received: August 1, 2008

AMS Subject Classification: 35K57, 35E99, 92D40

Key Words and Phrases: instability, self-diffusion, cross-diffusion

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 46
Issue: 4