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Publications


2018

Richard Ombaki, Kerongo J, Okwoyo J.  2018.  Formulated discrete mathematical model for delayed particle flow in cascaded sub-surface water reservoirs. AbstractWebsite

Pollution of sub-surface water reservoirs mainly rivers, streams, ponds and dams through contaminated water point sources (CWPS) was studied. The objectives were to formulate a discrete time delay mathematical model which describes the dynamics of reservoir pollution using mixing-problem processes that involve single species contaminants such as nutrients, pesticides, insecticides, herbicides and detergents. A conceptual perspective of mixing problem process in water tanks was applied to model delayed particle flow in cascaded water reservoir systems. The concentration (x) of pollutants was expressed as a function of the inflow and outflow rates using the principle for the conservation of mass. Systems of ODEs were generated from principles of mixing problems and then refined into a system of DDEs so that the concentration of pollutant leaving the reservoir at time t would be determined at some earlier

2011

  2011.  An algorithm for a discretized constrained, continuous Quadratic Contol Problem. Journal of Mathematical Sciences. 2(22):83-93.
  2011.  Stability and Persistence of Synchronized Manifold of Diffusively Coupled Oscillators. Far East Journal Of Dynamical Systems. 2(15):113-128.

2010

Okwoyo, J, Pokhariyal GP, Kinyanjui M, Okelo J.  2010.  Stability and persistence of synchronized manifold of diffusively coupled oscillators. AbstractWebsite

The study of Synchronization, Stability and Robustness of a system of oscillators has attracted great interest because of its application in many fields such as Neurobiology and Biological Systems [5, 6], Communication Systems [14], Mechanical and Electrical Systems [1], Stabilization of Unstable Periodic Orbits [18] and many others. In this paper, we study the condition for stability and persistence of synchronized manifold of diffusively coupled oscillators of linear and planar simple Bravais lattices. We considered "" d-dimensional oscillators each with an asymptotically stable limit cycle coupled by a near neighbor linear diffusive like path. We will state and prove a theorem that gives the conditions for stability and persistence of the synchronized manifold. The invariant manifold theory and Lyapunov exponents enabled us to establish the range of coupling strength for stability and robustness of the synchronized state. The comparison of the trajectories of oscillators in the manifolds was by comparing the amplitudes of graphed trajectories generated using ode45 Matlab solver.

  2010.  Mode locking (synchronization) in a coupled two sector model. Journal of Mathematical Sciences. 4(21):483-491.

2008

okwoyo james.  2008.  Couette Flow Between two Parallel Infinite plates in the Presence of Transverse Magnetic field. Journal of Kenya Mateorological Society. 1(1):34-56.
okwoyo james.  2008.  Synchronization of all-to-all Coupled Oscillators. journal of Mathematical sciences. 2(19):239-252.

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