رسائل الماجستير

رسائل الماجستير الصادرة عن قسم الرياضيات بكلية العلوم والآداب

استعراض

استعراض Master Theses | رسائل الماجستير بواسطة الموضوع "Bacterial Competition"



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  • صورة مصغرة
    مادة
     رسالة جامعية
    مقيد
    Mathematical Modeling of Bacterial Competition and Antibiotic Resistance Dynamics in a Chemostat
    (جامعه نجران;2026 )
    Numerical Simulations • Bacterial Competition • Mathematical Modeling
    This thesis analytically studies four hierarchical chemostat models, formulated as sys tems of ordinary differential equations of increasing dimension (2D, 3D, 4D, and 5D), representing single-species growth, two-species competition, single-antibiotic inhibition, and multi-antibiotic inhibition, respectively. For each model, all equilibrium points are derived analytically with their existence conditions, the Jacobian matrix is computed, and local stability is analyzed through the eigenvalue spectrum, applying the Routh–Hurwitz criterion for characteristic equations of orders two through four. The analytical results are validated numerically in MATLAB and Python through phase portraits, time series, and bifurcation diagrams. Themain results show that in the three-dimensionalmodel, thetwonon-zeroequilibria cannot be simultaneously stable, providing a mathematical demonstration of the competi tive exclusion principle. Introducing a fourth and fifth variable in the higher-dimensional models alters the stability conditions and raises the order of the characteristic equation accordingly, with equilibrium stability in the five-dimensional model determined after matrix reduction. Comparative analysis across the four models quantifies how increasing model complexity reshapes the equilibrium structure and stability regions.