%0 Journal Article %T Turing instability in two-patch predator-prey population dynamics %A Al-Qahtani, Ali %A Almoeed, Aesha %A Najmi, Bayan %A Aly, Shaban %J Journal of Mathematics and Computer Science %D 2018 %V 18 %N 3 %@ ISSN 2008-949X %F Al-Qahtani2018 %X In this paper, a spatio-temporal model as systems of ODE which describe two-species Beddington-DeAngelis type predator-prey system living in a habitat of two identical patches linked by migration is investigated. It is assumed in the model that the per capita migration rate of each species is influenced not only by its own but also by the other one's density, i.e., there is cross diffusion present. We show that a standard (self-diffusion) system may be either stable or unstable, a cross-diffusion response can stabilize an unstable standard system and destabilize a stable standard system. For the diffusively stable model, numerical studies show that at a critical value of the bifurcation parameter the system undergoes a Turing bifurcation and the cross migration response is an important factor that should not be ignored when pattern emerges. %9 journal article %R 10.22436/jmcs.018.03.01 %U http://dx.doi.org/10.22436/jmcs.018.03.01 %P 255--261 %0 Book %T The Geometry of Ecological Interaction: Simplifying Spatial Complexity %A U. Dieckmann %A R. Law %A J. A. Metz %D 2005 %I Cambridge University Press %C Cambridge %F Dieckmann2005 %0 Journal Article %T Two ways of modeling cross diffusion %A M. Farkas %J Nonlinear Anal. %D 1997 %V 30 %F Farkas1997 %0 Book %T Dynamical Models in Biology %A M. Farkas %D 2001 %I Academic Press %C San Diego %F Farkas2001 %0 Journal Article %T Interspecific influence on mobility and Turing instability %A Y. Huang %A O. Diekmann %J Bull. Math. Biol. %D 2003 %V 65 %F Huang2003 %0 Book %T Mathematical Biology %A J. D. Murray %D 1989 %I Springer-Verlag %C Berlin %F Murray 1989 %0 Book %T Global Dynamical Properties of Lotka-Volterra system %A Y. Takeuchi %D 1996 %I World Scientific Publishing Co. %C Singapore %F Takeuchi1996 %0 Journal Article %T The chemical basis of morphogenesis %A A. M. Turing %J Philos. Trans. Roy. Soc. London Ser. B %D 1952 %V 237 %F Turing1952