According to Milankovitch theory of ice ages, glacial cycles are driven by
variations in the insolation, i.e. the amount of the incoming solar radiation
reaching the Earth. These variations are associated with variations of the
Earth's orbit. Many attempts have been made to identify the in
uence of
the orbital variations on Earth's climate; however, the knowledge and tools
needed to complete a unied theory for ice ages have not been developed
yet.
Here, we focus on the climatic variations that have occurred over the
last few million years. Paleoclimatic records show that the glacial cycles
are linked to the orbitally driven variations in insolation. However, the
relationship is far from linear, and insolation alone can not explain the
climatic variability seen in the records.
In the rst part of this thesis, we discuss the possible dynamical mechanisms
for linking the frequencies observed in the records to those present in
the astronomical forcing. We shall do this in terms of a general framework
of conceptual dynamical models, which may or may not exhibit internal
self-sustained oscillations. We introduce and discuss two distinct mechanisms
for a periodic response at a dierent period to a periodic forcing. In
one case, the system has the ability of maintaining internal oscillations. In
the second case, the system is damped, so it does not possess self-sustained
oscillations.
The distinction between the two scenarios mentioned above is understood
in terms of two phenomena in oscillating systems, namely the phenomenon
of resonance and that of synchronisation. To avoid confusion between them,
we illustrate the main dierences, and present a listing of their characteristic
properties. A Dung and a Dung-Van der Pol oscillator have been used
for illustrative purposes.
The second part of this thesis addresses the analysis of nonlinear resonances
in a weakly-damped Dung oscillator. In addition to already known
odd and even subharmonic resonances, we combine the physical concept of
subharmonic resonances and mathematical concept of bifurcations to uncover
a novel resonance type.
In the last section, we discuss a third possible mechanism for the climate
response to an external periodic forcing. In this scenario, the system is
excitable: a small perturbation from the xed point may produce large
excursions.