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Delay differential equations in engineering
Zlámal, Ondřej ; Řehák, Pavel (referee) ; Opluštil, Zdeněk (advisor)
This thesis is about dynamical systems and analysis of their stability. These systems are described using delayed differential equations, whose character is ideal for describing many real life problems. In this thesis it is analysed how size of delay and its rate affects stability of system. Change of stability in system is traced using Hopf bifurcations. Theory of this thesis will be applied on system based on machine tool vibrations and system describing feedback in lasers.
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Linear theory of delayed differential equations
Marková, Hana ; Pražák, Dalibor (advisor) ; Kaplický, Petr (referee)
It the thesis, we study retarded functional differential equations. As a result of the Banach fixed point theorem, it is easy to show that there exists a unique solution to such problems. Alas, this theorem gives us no information on the form of the solution. Therefore, we are particularly interested in expressing it. We achieve that by applying Laplace transform to both sides of the equation, we get a solution to this modified problem and subsequently claim that we can apply the inverse Laplace transform to express the solution of the former problem. At the end of the thesis, we formulate and prove the exponential estimate of the solution. 1
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