International Scientific Research PublicationsJournal of Mathematics and Computer Science(JMCS) ISSN 2008-949X18320180222Turing instability in two-patch predator-prey population dynamics255261http://dx.doi.org/10.22436/jmcs.018.03.01ENAli Al-QahtaniDepartment of Mathematics, Faculty of Science, King Khalid University, Saudi ArabiaAesha AlmoeedDepartment of Mathematics, Faculty of Science, King Khalid University, Saudi ArabiaBayan NajmiDepartment of Mathematics, Faculty of Science, King Khalid University, Saudi ArabiaShaban AlyDepartment of Mathematics, Faculty of Science, King Khalid University, Saudi Arabia \(\&\) Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, EgyptIn 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.http://www.isr-publications.com/jmcs/6811/download-turing-instability-in-two-patch-predator-prey-population-dynamicsInternational Scientific Research PublicationsJournal of Mathematics and Computer Science(JMCS) ISSN 2008-949X18320180322\(F_{m}\)-contractive and \(F_{m}\)-expanding mappings in \(M\)-metric spaces262271http://dx.doi.org/10.22436/jmcs.018.03.02ENNabil MlaikiDepartment of Mathematics and General Sciences, Prince Sultan University, Riyadh, 11586, Saudi ArabiaInspired by the work of Górnicki in his recent article [J. Górnicki, Fixed Point Theory Appl., \({\bf 2017}\) (2017), 10 pages], where he introduced a new class of self mappings
called \(F\)-expanding mappings, in this paper we introduce the concept of \(F_{m}\)-contractive and
\(F_{m}\)-expanding mappings in \(M\)-metric spaces. Also, we prove the existence and uniqueness of fixed point for such mappings.http://www.isr-publications.com/jmcs/6915/download-f-m-contractive-and-f-m-expanding-mappings-in-m-metric-spaces