Browsing by Author "Ireri, Jane"

Now showing 1 - 4 of 4
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    Chemostat Model with Periodic Nutrient Input Described by Fourier Series
    (Asian Research Journal of Mathematics, 2020) Moindi, Stephene; Ireri, Jane; Pokhariyal, Ganesh
    In this paper we present a periodic Chemostat model of two species competing for a single nutrient available in limiting supply. The nutrient input is varied periodically using a Fourier series function to take into account the changing patterns as seasons vary. We show both analytically and numerically that varying the nutrient input using a Fourier Series function results in a better model to describe coexistence of species in natural environments.
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    Delayed Nutrient Conversion for a Single Species Periodic Chemostat
    (Journal of Scientific Research & Reports, 2020) Moindi, Stephene; Ireri, Jane; Pokhariyal, Ganesh
    In this paper we analyze a Chemostat model with periodic nutrient input modelled using Fourier series and incorporate delays in nutrient conversion. We show that both periodicity and delays have complementing influence in the long term behaviour of the species. Numerical results show that periodicity has bigger influence on species density variations for delays below the Hopf Bifurcation point, while for delays above the Bifurcation point,the delay effect is more influential
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    Hopf Bifurcation Analysis for a Two Species Periodic Chemostat Model with Discrete Delays
    (Journal of Advances in Mathematics and Computer Science, 2020) Moindi, Stephene; Ireri, Jane; Pokhariyal, Ganesh
    In this paper we analyze a Chemostat model of two species competing for a single limiting nutrient input varied periodically using a Fourier series with discrete delays. To understand global aspects of the dynamics we use an extension of the Hopf bifurcation theorem, a method that rigorously establishes existence of a periodic solution. We show that the interior equilibrium point changes its stability and due to the delay parameter it undergoes a Hopf bifurcation. Numerical results shows that coexistence is possible when delays are introduced and Fourier series produces the required seasonal variations. We also show that for small delays periodic variations of nutrients has more influence on species density variations than the delay.
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    Laplace Transform Solution of Hydromagnetic Steady Flow of Viscous Incompressible Fluid Between Two Infinite Parallel Plates.
    (2010-07) Ireri, Jane
    Hydromagnetics involves the effect of externally impressed magnetic field on the onset of thermal instability in electrically conducting fluids. In broad terms, the subject of hydromagnetics is concerned with the ways in which magnetic fields can affect fluid behavior. These fluids include liquid metals and highly ionized gas-like substances called plasmas. When we consider a fluid which has the property of electrical conduction; and suppose also that magnetic fields are prevalent. The electrical conductivity of the fluid and the prevalence of magnetic fields contribute to effects of two kind: first, by motion of the electrically conducting fluid across the magnetic lines of force, electric currents are generated and the associated magnetic fields contribute to changes in the existing fields; and second, the fact that the fluid elements carrying currents transverse magnetic lines of force contributes to additional forces acting on the fluid elements. It is in this two fold interaction between the motions and the fields that is responsible for patterns of behavior which are often unexpected and striking.