1,396 research outputs found
Chaos in neural networks with a nonmonotonic transfer function
Time evolution of diluted neural networks with a nonmonotonic transfer
function is analitically described by flow equations for macroscopic variables.
The macroscopic dynamics shows a rich variety of behaviours: fixed-point,
periodicity and chaos. We examine in detail the structure of the strange
attractor and in particular we study the main features of the stable and
unstable manifolds, the hyperbolicity of the attractor and the existence of
homoclinic intersections. We also discuss the problem of the robustness of the
chaos and we prove that in the present model chaotic behaviour is fragile
(chaotic regions are densely intercalated with periodicity windows), according
to a recently discussed conjecture. Finally we perform an analysis of the
microscopic behaviour and in particular we examine the occurrence of damage
spreading by studying the time evolution of two almost identical initial
configurations. We show that for any choice of the parameters the two initial
states remain microscopically distinct.Comment: 12 pages, 11 figures. Accepted for publication in Physical Review E.
Originally submitted to the neuro-sys archive which was never publicly
announced (was 9905001
Prescriptions in Loop Quantum Cosmology: A comparative analysis
Various prescriptions proposed in the literature to attain the polymeric
quantization of a homogeneous and isotropic flat spacetime coupled to a
massless scalar field are carefully analyzed in order to discuss their
differences. A detailed numerical analysis confirms that, for states which are
not deep in the quantum realm, the expectation values and dispersions of some
natural observables of interest in cosmology are qualitatively the same for all
the considered prescriptions. On the contrary, the amplitude of the wave
functions of those states differs considerably at the bounce epoch for these
prescriptions. This difference cannot be absorbed by a change of
representation. Finally, the prescriptions with simpler superselection sectors
are clearly more efficient from the numerical point of view.Comment: 18 pages, 6 figures, RevTex4-1 + BibTe
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