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://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://isr-publications.com/jmcs/6915/download-f-m-contractive-and-f-m-expanding-mappings-in-m-metric-spacesInternational Scientific Research PublicationsJournal of Mathematics and Computer Science(JMCS) ISSN 2008-949X18320180413Explicit solution for some generalized fluids in laminar flow with slip boundary conditions272281http://dx.doi.org/10.22436/jmcs.018.03.03ENMourad ChamekhMathematics Department, Colleges of Science and Arts, AlKamel, University of Jeddah, KSA \(\&\) University of Tunis El Manar, National Engineering School at Tunis, LAMSIN, 1002, Tunis, TunisiaTarig. M. ElzakiMathematics Department, Colleges of Science and Arts, AlKamel, University of Jeddah, KSAIn this study, we present a new approximation method to give an explicit solution of a laminar flow using a Sisko
model. This is a problem of a generalized Newtonian fluid with slip boundary conditions. The proposed method
is based on the variational iteration method (VIM) combined with an approximation step. This method is validated
where the exact solution is available. In addition, in order to enrich the discussion, a numerical method is
presented. The results illustrate that the VIM may be more effective that the finite difference method for a dilatant
fluid. However, the VIM will be inappropriate for pseudoplastic fluid cases.
http://isr-publications.com/jmcs/7005/download-explicit-solution-for-some-generalized-fluids-in-laminar-flow-with-slip-boundary-conditionsInternational Scientific Research PublicationsJournal of Mathematics and Computer Science(JMCS) ISSN 2008-949X18320180425On upper and lower \((\tau_1,\tau_2)\)-precontinuous multifunctions282293http://dx.doi.org/10.22436/jmcs.018.03.04ENChawalit BoonpokMathematics and Applied Mathematics Research Unit, Department of Mathematics, Faculty of Science, Mahasarakham University, Mahasarakham, 44150, ThailandChokchai ViriyapongMathematics and Applied Mathematics Research Unit, Department of Mathematics, Faculty of Science, Mahasarakham University, Mahasarakham, 44150, ThailandMontri ThongmoonMathematics and Applied Mathematics Research Unit, Department of Mathematics, Faculty of Science, Mahasarakham University, Mahasarakham, 44150, ThailandThis paper deals with the concepts of upper and lower
\((\tau_1,\tau_2)\)-precontinuous multifunctions.
Some characterizations of upper and lower \((\tau_1,\tau_2)\)-precontinuous multifunctions are investigated. The relationships between upper and lower \((\tau_1,\tau_2)\)-precontinuous multifunctions and the other types of continuity are discussed.http://isr-publications.com/jmcs/7039/download-on-upper-and-lower-tau-1tau-2-precontinuous-multifunctionsInternational Scientific Research PublicationsJournal of Mathematics and Computer Science(JMCS) ISSN 2008-949X18320180427Mathematical models of the Spread of Malaria with the vertical transmission (congenital malaria)294305http://dx.doi.org/10.22436/jmcs.018.03.05ENEbrahim As-ShareefSchool of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. ChinaArif SaifSchool of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. ChinaCui-Hong YangSchool of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. ChinaXin-An ZhangSchool of Mathematics and Statistics, Central China Normal University, Wuhan 430079, P. R. ChinaThe main goal of this paper is to develop a mathematical model to study the dynamic of malaria transmission, and the direct effects of congenital malaria on the spread of malaria.
In this study, we have clarified the significant impact of malaria on the human community through their impact on the newborn, and that directly increases spread of the malaria in the human community, especially in the newborns with the lower and inexperienced immunity systems.
The existence and stability of the disease-free points of the system is analyzed. We established that the disease-free equilibrium point is locally asymptotically stable when the reproduction number \(R_{0}<1\) and the disease always dies out. For \(R_{0}>1\) the disease-free equilibrium becomes unstable and there exists a unique endemic equilibrium.http://isr-publications.com/jmcs/7044/download-mathematical-models-of-the-spread-of-malaria-with-the-vertical-transmission-congenital-malaria