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Delay Differential Equations in Dynamic Systems
Dokyi, Martha ; Šremr, Jiří (oponent) ; Opluštil, Zdeněk (vedoucí práce)
This thesis is a review of Delay Differential Equations in Dynamical systems. Starting with a general overview of Delay Differential Equations, we present the concept on Delay Differentials and the application of its models, ranging from biology and population dynamics to physics and engineering. We will also give an overview on Dynamical systems and delay differential equations in the dynamic systems .An area for modelling with delay differentials equations is Epidemiology. Emphasis is given to the development of the Susceptible-Infected-Removed(SIR) epidemiological model without and with time delay. We the analyse our two models under equilibra and local stability using assumed data of COVID -19 .Results would be compared between the model without delays and model with delays.
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Delay Differential Equations in Dynamic Systems
Dokyi, Martha ; Šremr, Jiří (oponent) ; Opluštil, Zdeněk (vedoucí práce)
This thesis is a review of Delay Differential Equations in Dynamical systems. Starting with a general overview of Delay Differential Equations, we present the concept on Delay Differentials and the application of its models, ranging from biology and population dynamics to physics and engineering. We will also give an overview on Dynamical systems and delay differential equations in the dynamic systems .An area for modelling with delay differentials equations is Epidemiology. Emphasis is given to the development of the Susceptible-Infected-Removed(SIR) epidemiological model without and with time delay. We the analyse our two models under equilibra and local stability using assumed data of COVID -19 .Results would be compared between the model without delays and model with delays.
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Analytical approaches of local stability investigation applied to piecewise linear vibrating system - Kelvin-Voigt impact oscillator
Kocanda, Lubomír
Dynamical behaviour of soft impact oscillator is multifarious with plenty of manifold behaviour kinds commensurated with system parameters. The stability analysis of soft impact oscillator is very important for dynamic investigation. Floquet theory or Ljapunov exponent approach can be applied in numerical integration. However, contrary to numerical integration results processing, the analytic-numerical approaches give better view of the dynamical nub despite its' facing mutual very diverse terms. Approaches based on eigenvalue problem and small difference method presented in authors past papers are eked out with this contribution. This paper aim is to obtain the result of the local stability investigation approaches in analytical form.
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