A mathematical model, coupling the dynamics of short-term stem-like cells and mature leukocytes in leukemia with that of the immune system, is investigated. The model is described by a system of seven delay differential equations with seven delays. Three equilibrium points E0, E1, E2 are highlighted. The stability and the existence of the Hopf bifurcation for the equilibrium points are investigated. In the analysis of the model, the rate of asymmetric division and the rate of symmetric division are very important.
A five-dimensional nonlinear mathematical model of the electrohydraulic servo(mechanism) is considered. In the system equilibria analysis, the critical case of a zero eigenvalue occurs. The Lyapunov-Malkin Theorem and Routh-Hurwitz criterion provide conditions for controllers to stabilize all relevant equilibria in the closed-loop system. Geometric control paradigm is then applied in synthesis and the performance of the obtained controlled system is numerically validated from viewpoint of the regulator classical problem.
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