Research ArticleOpen accessIn the keywordsBifurcation and Stability Analysis of a Food Web in a ChemostatS.M. Sohel RanaIn this study, a classical model describing a food web in a chemostat involving three species competing for non-reproducing, growth rate-limiting nutrient in which one of the competitors predates on one of the other competitors is considered. Quantitative analyses of non-negativity and boundedness of solution trajectories, dissipativity, behavior around equilibria, global stability and persistence of the model equations are analyzed. … …Journal of Mathematics and Statistics, Vol. 12, Issue 4 · 22 Oct 2016 · 7,081 accessesView PDFCite
Research ArticleOpen accessIn the keywordsBIFURCATION ANALYSIS OF EQUILIBRIUM POINT IN TWO NODE POWER SYSTEMHalima Aloui, Faouzi Bacha, Moncef GasmiThis study presents a study of bifurcation in a dynamic power system model. It becomes one of the major precautions for electricity suppliers and these systems must maintain a steady state in the neighborhood of the operating points. We study in this study the dynamic stability of two node power systems theory and the stability of limit cycles emerging from … …American Journal of Applied Sciences, Vol. 11, Issue 4 · 29 Jan 2014 · 7,055 accessesView PDFCite
Research ArticleOpen accessIn the keywordsOn Stability and Bifurcation of Solutions of Nonlinear System of Differential Equations for AIDS DiseaseS. A.A. El-MaroufProblem statement: This study aims to discuss the stability and bifurcation of a system of ordinary differential equations expressing a general nonlinear model of HIV/AIDS which has great interests from scientists and researchers on mathematics, biology, medicine and education. The existance of equilibrium points and their local stability are studied for HIV/AIDS model with two forms of the incidence rates. … …American Journal of Applied Sciences, Vol. 9, Issue 7 · 24 Apr 2012 · 7,018 accessesView PDFCite
Research ArticleOpen accessIn the keywordsOn the Dynamics of a General Predator-Prey SystemM. M.A. El-Sheikh, S. A.A. El-Marouf, Z. M. AlaofyProblem statement: In this study a general two dimensional predator-prey model is considered. The dynamic and existence of equilibrium points are studied. Conclusion/Recommendations: Hopf bifurcation is discussed. The existence and uniqueness of limit cycles is proved. Special cases are considered to justify our results. …Journal of Mathematics and Statistics, Vol. 7, Issue 4 · 28 Oct 2011 · 7,322 accessesView PDFCite
Research ArticleOpen accessIn the abstractTowards Some General Ecological PrinciplesArild WikanDiscrete deterministic age-structured, stage-structured and difference delay equation population models are analysed and compared with respect to stability and nonstationary behaviour. All three models show that species with iteroparous life histories tend to be more stable than species with semelparous life histories which allow us to conclude that this must be a fairly general ecological principle. Considering iteroparity, the precocious … …Journal of Mathematics and Statistics, Vol. 8, Issue 4 · 3 Jan 2013 · 6,929 accessesView PDFCite
Research ArticleOpen accessIn the abstractGlobal Analysis of an Epidemic Model with Non-Linear Incidence RateS. A.A. El-Marouf, S. M. AlihabyProblem statement: In this study the equilibrium points and their local stability are found for SIQ and SIQR epidemic models with three forms of the incidence rates. Also, we study the global stability of the equilibrium by constructing the new forms of Liapounov functions. Conclusion/Recommendations: We explored the existence of Hopf bifurcation for some parameters in the given model. …Journal of Mathematics and Statistics, Vol. 7, Issue 4 · 28 Oct 2011 · 7,274 accessesView PDFCite
Research ArticleOpen accessIn the abstractPeriodic and Non Periodic (Complex) Behavior of a Model of Bioreactor With Cell RecyclingG. Ibrahim, M. A. Ramadan, S. A.A. El-Marouf, A. M. Al-MahdiA structured model of bioreactor for an activated sludge process was presented. The stability and bifurcation characteristics of the model are investigated, the bifurcation analysis of the model shows static and complex dynamic behavior (periodic and complex) over a wide range of the model parameters. The model exhibits a new interesting behavior (in some range of parameters) including four static … …Journal of Mathematics and Statistics, Vol. 3, Issue 1 · 31 Mar 2007 · 6,776 accessesView PDFCite