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Realizations of mathematical model of wind turbulations as lumped electronic circuits
Bürger, David ; Šotner, Roman (referee) ; Petržela, Jiří (advisor)
This semester work deals with implementation of the mathematical model known as modified Lorenz system as an electronic circuit with lumped parameters. Dynamical system is autonomous, deterministic and is described by a set of first-order ordinary differential equations. Our aim is to derive three different circuitry realizations each having specific properties. In the first case realization is canonical in the sense of the integrator block conception where the internal system parameters are adjusted by three potentiometers. Second realization represents modification towards independent adjustment of all four system parameters and, consequently, to tracing dynamical evolution of model solution. Last oscillator, on the contrary to previous circuits, work in current mode rather than voltage regime.
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Stability and chaotic behaviour of the Lorenz system
Oborná, Eliška ; Nechvátal, Luděk (referee) ; Čermák, Jan (advisor)
This bachelor's thesis analyzes the behavior of the Lorenz's model of convective flow in the atmosphere depending on the Rayleigh number. It offers several methods when analyzing stability of nonlinear systems of the first order autonomous differential equations. Part of the work also consists of introduction to deterministic chaos which appears in dynamic systems with a parameter. The work is supported by graphic interpretation of a stable and chaotic behavior by using the software Maple.
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Nonlinear dynamical systems and chaos
Tesař, Lukáš ; Opluštil, Zdeněk (referee) ; Nechvátal, Luděk (advisor)
The diploma thesis deals with nonlinear dynamical systems with emphasis on typical phenomena like bifurcation or chaotic behavior. The basic theoretical knowledge is applied to analysis of selected (chaotic) models, namely, Lorenz, Rössler and Chen system. The practical part of the work is then focused on a numerical simulation to confirm the correctness of the theoretical results. In particular, an algorithm for calculating the largest Lyapunov exponent is created (under the MATLAB environment). It represents the main tool for indicating chaos in a system.
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Nonlinear dynamical systems and chaos
Tesař, Lukáš ; Opluštil, Zdeněk (referee) ; Nechvátal, Luděk (advisor)
The diploma thesis deals with nonlinear dynamical systems with emphasis on typical phenomena like bifurcation or chaotic behavior. The basic theoretical knowledge is applied to analysis of selected (chaotic) models, namely, Lorenz, Rössler and Chen system. The practical part of the work is then focused on a numerical simulation to confirm the correctness of the theoretical results. In particular, an algorithm for calculating the largest Lyapunov exponent is created (under the MATLAB environment). It represents the main tool for indicating chaos in a system.
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Realizations of mathematical model of wind turbulations as lumped electronic circuits
Bürger, David ; Šotner, Roman (referee) ; Petržela, Jiří (advisor)
This semester work deals with implementation of the mathematical model known as modified Lorenz system as an electronic circuit with lumped parameters. Dynamical system is autonomous, deterministic and is described by a set of first-order ordinary differential equations. Our aim is to derive three different circuitry realizations each having specific properties. In the first case realization is canonical in the sense of the integrator block conception where the internal system parameters are adjusted by three potentiometers. Second realization represents modification towards independent adjustment of all four system parameters and, consequently, to tracing dynamical evolution of model solution. Last oscillator, on the contrary to previous circuits, work in current mode rather than voltage regime.
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Stability and chaotic behaviour of the Lorenz system
Oborná, Eliška ; Nechvátal, Luděk (referee) ; Čermák, Jan (advisor)
This bachelor's thesis analyzes the behavior of the Lorenz's model of convective flow in the atmosphere depending on the Rayleigh number. It offers several methods when analyzing stability of nonlinear systems of the first order autonomous differential equations. Part of the work also consists of introduction to deterministic chaos which appears in dynamic systems with a parameter. The work is supported by graphic interpretation of a stable and chaotic behavior by using the software Maple.
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Characteristics of the Chen Attractor
Augustová, Petra ; Beran, Zdeněk
Within the paper a mathematical representation of the so-called Chen model is described as a particular parametric three-dimensional chaotic dynamical system, i.e. a system of three nonlinear differential equations evolving in time. The main aim of this paper is to find for the Chen system the properties that are known for the Lorenz system and its famous Lorenz attractor. First, the integrals of motion are derived for some parameters of the Chen system. The integrals of motions play an important role in physics, e.g. for conservation laws. Next, the shape of the global attractor of this system is approximated by volumes that contain the attractor. The shape predicts the future behavior of the system. To obtain these results, the already proved fact that the Chen system is a continued transition of the Lorenz system is used. According to our knowledge, the same approach of shifting the known facts about the Lorenz system to a newdynamical system, the Chen system in this context, has not been presented yet.
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