| dc.contributor |
Ashwin, Peter |
|
| dc.contributor |
Holland, Mark |
|
| dc.creator |
Alraddadi, I |
|
| dc.date |
2022-09-27T09:47:19Z |
|
| dc.date |
2022-09-26 |
|
| dc.date |
2022-09-27T08:54:08Z |
|
| dc.date |
2022-09-27T09:47:19Z |
|
| dc.date.accessioned |
2023-02-23T12:16:53Z |
|
| dc.date.available |
2023-02-23T12:16:53Z |
|
| dc.identifier |
http://hdl.handle.net/10871/130986 |
|
| dc.identifier.uri |
http://localhost:8080/xmlui/handle/CUHPOERS/258646 |
|
| dc.description |
This thesis is motivated by study of long timescale variability of the climate system.
We focus on two models of nonlinear behaviour that are used in climate modelling.
The first of these models is the forced van der Pol oscillator, motivated by examination
of the Pleistocene ice age oscillations forced by astronomical orbital variations. The
second of these is the long timescale carbon cycle model of Rothman [1].
In Chapters 2-4, we discuss unforced and forced van der Pol oscillators, following the
analysis of Guckenheimer et al. [2] for periodically cases. We use a geometric singular
perturbation theory (GSPT) approach of [2] to reduce to the dynamics of the return
map and extend to their work to construct return maps for quasiperiodically forced
cases. We note this return map can be noninvertible in various values to the parameters.
In the remaining chapters, we study the dynamics of a recent model of Rothman for
long timescale carbon cycle. We reproduce and extend various results of the Rothman
model. In particular, we numerically find normal forms of Bautin bifurcations to
confirm their criticality. We also extend the analysis of the normal form coefficients to
identify where the fold limit cycle bifurcation occurs. |
|
| dc.publisher |
University of Exeter |
|
| dc.publisher |
Mathematics |
|
| dc.rights |
2024-03-26 |
|
| dc.rights |
I wish to publish papers using material that is substantially drawn from my thesis - embargo until 26/3/24 |
|
| dc.rights |
http://www.rioxx.net/licenses/all-rights-reserved |
|
| dc.title |
Nonlinear Oscillator Models for Long-Timescale Climate Variability |
|
| dc.type |
Thesis or dissertation |
|
| dc.type |
PhD in Mathematics |
|
| dc.type |
Doctoral |
|
| dc.type |
Doctoral Thesis |
|