An in depth study of temporal chaotic systems, both
discrete and continuous, is presented. The techniques for
the characterization of chaotic attractors are: Lyapunov
stability, dimension spectra and unstable periodic orbits.
Comparison of numerical and analytical methods clarify some
of the limitations of these techniques. A two dimensional
hyperbolic baker map with a complete set of unstable orbits
is examined. The evolution of structure and changes in the
f(a) spectrum for this map are related to changes in an
underlining Cantor set. Numerical calculation of unstable
periodic orbits for a related baker map with an incomplete
set of unstable orbits allow the investigation of the
properties of a pruned Cantor set. The effects of the
pruning on the associated f(a) spectrum are investigated.
It is also shown that the unstable manifold of a hyperbolic
toral map does not wind densely around the torus, but
consists of an infinite number of line segments. This
facilitates the efficient computation of the dimension
spectrum through a rotation of this manifold. A new
structure not previously observed m discrete systems is
characterized. Intermittency theory previously applied to
dissipative systems is applied to a variety of two
dimensional non-dissipative systems. A new type of
intermittency is found from a detailed comparison between
existing theory and numerical experiments. The important
and unresolved problem of the correspondence between
continuous and discrete systems is investigated using
analytical and numerical techniques. Properties of the
chaotic attractors of infinite dimensional delayed
differential equations are examined as a function of the
time delay and nonlinearity parameters.
Item Type:
Thesis (PhD)
Date of Award:
1993
Refereed:
No
Supervisor(s):
Heffernan, Daniel M.
Uncontrolled Keywords:
Chaotic behavior in systems; Temporal chaotic systems; Chaos theory