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Linear difference equations: stability analysis
Tesař, Lukáš ; Dosoudilová, Monika (referee) ; Tomášek, Petr (advisor)
This thesis deals with asymptotic stability investigation of linear difference equation. The Schur-Cohn criterion and discrete Routh-Schur criterion are introduced and demonstrated on several examples. Both criterions are implemented in Maple programming enviroment. Boundary locus technique is illustrated on a stability analysis of the Adams-Bashforth method for numerical solving of an initial value problem of first order ordinary differential equation.
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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.
|
|
|
Linear difference equations: stability analysis
Tesař, Lukáš ; Dosoudilová, Monika (referee) ; Tomášek, Petr (advisor)
This thesis deals with asymptotic stability investigation of linear difference equation. The Schur-Cohn criterion and discrete Routh-Schur criterion are introduced and demonstrated on several examples. Both criterions are implemented in Maple programming enviroment. Boundary locus technique is illustrated on a stability analysis of the Adams-Bashforth method for numerical solving of an initial value problem of first order ordinary differential equation.
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