For EDITORS

For READERS

All Issues

Vol.10, 2020
Vol.9, 2019
Vol.8, 2018
Vol.7, 2017
Vol.6, 2016
Vol.5, 2015
Vol.4, 2014
Vol.3, 2013
Vol.2, 2012
Vol.1, 2011
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.
PDF      Download reader