| Volume 1, Number 1, 2011, Pages 95-120 DOI：10.11948/2011007 |
| Cross-diffusion induced instability and stability in reaction-diffusion systems |
| Junping Shi,Zhifu Xie,Kristina Little |
| Keywords: |
| Abstract: |
| In a reaction-diffusion system, diffusion can induce the instability of a uniform equilibrium which is stable with respect to a constant perturbation, as shown by Turing in 1950s. We show that cross-diffusion can destabilize a uniform equilibrium which is stable for the kinetic and self-diffusion reaction systems; on the other hand, cross-diffusion can also stabilize a uniform equilibrium which is stable for the kinetic system but unstable for the self-diffusion reaction system. Application is given to predator-prey system with preytaxis and vegetation pattern formation in a water-limited ecosystem. |
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