Pelzer, Anouk F. G. (2020) Variations of the Lorenz-96 model. Master's Thesis / Essay, Mathematics.
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Abstract
In this thesis we will investigate the differences between the Lorenz-96 model and its modifications. We obtain these modifications by changing the structure of the nonlinear terms in the Lorenz-96 model. We will treat the general modified model and three specific systems and compare these with the Lorenz-96 model. To determine the dynamics of the models, we will study the eigenvalues of the Jacobian matrix at the trivial equilibrium, Lyapunov coefficients to distinguish between sub- and supercritical Hopf bifurcations, Lyapunov exponents to determine when there is chaos etc. Some of the results are that in the Lorenz-96 model there are no escaping orbits, while this is only true under some conditions for the modified systems. Furthermore there are differences in bifurcations. The external forcing F appearing in the equations of all these models can be used as a bifurcation parameter. The trivial equilibrium is always stable when F is zero for every model. For F<0 some modifications has a stable trivial equilibrium, while this is not the case for the original model. For this model there only occur first Hopf bifurcations when F is positive, but for its modifications there can be other (first) bifurcations too, like a Pitchfork bifurcation. There are even bifurcations occuring for these modified systems, while these don't appear in the Lorenz-96 model, such as degenerate bifurcations meaning that suddenly there appear simultaneously more than one equilibrium at the same F.
| Item Type: | Thesis (Master's Thesis / Essay) |
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| Supervisor name: | Sterk, A.E. and Waalkens, H. |
| Degree programme: | Mathematics |
| Thesis type: | Master's Thesis / Essay |
| Language: | English |
| Date Deposited: | 02 Jul 2020 13:36 |
| Last Modified: | 02 Jul 2020 13:36 |
| URI: | https://fse.studenttheses.ub.rug.nl/id/eprint/22370 |
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