25,135 research outputs found
Resonance bifurcations from robust homoclinic cycles
We present two calculations for a class of robust homoclinic cycles with
symmetry Z_n x Z_2^n, for which the sufficient conditions for asymptotic
stability given by Krupa and Melbourne are not optimal.
Firstly, we compute optimal conditions for asymptotic stability using
transition matrix techniques which make explicit use of the geometry of the
group action.
Secondly, through an explicit computation of the global parts of the Poincare
map near the cycle we show that, generically, the resonance bifurcations from
the cycles are supercritical: a unique branch of asymptotically stable period
orbits emerges from the resonance bifurcation and exists for coefficient values
where the cycle has lost stability. This calculation is the first to explicitly
compute the criticality of a resonance bifurcation, and answers a conjecture of
Field and Swift in a particular limiting case. Moreover, we are able to obtain
an asymptotically-correct analytic expression for the period of the bifurcating
orbit, with no adjustable parameters, which has not proved possible previously.
We show that the asymptotic analysis compares very favourably with numerical
results.Comment: 24 pages, 3 figures, submitted to Nonlinearit
Phase resetting effects for robust cycles between chaotic sets
In the presence of symmetries or invariant subspaces, attractors in dynamical systems can become very complicated owing to the interaction with the invariant subspaces. This gives rise to a number of new phenomena including that of robust attractors showing chaotic itinerancy. At the simplest level this is an attracting heteroclinic cycle between equilibria, but cycles between more general invariant sets are also possible.
This paper introduces and discusses an instructive example of an ODE where one can observe and analyse robust cycling behaviour. By design, we can show that there is a robust cycle between invariant sets that may be chaotic saddles (whose internal dynamics correspond to a Rossler system), and/or saddle equilibria.
For this model, we distinguish between cycling that include phase resetting connections (where there is only one connecting trajectory) and more general non-phase resetting cases where there may be an infinite number (even a continuum) of connections. In the non-phase resetting case there is a question of connection selection: which connections are observed for typical attracted trajectories? We discuss the instability of this cycling to resonances of Lyapunov exponents and relate this to a conjecture that phase resetting cycles typically lead to stable periodic orbits at instability whereas more general cases may give rise to `stuck on' cycling.
Finally, we discuss how the presence of positive Lyapunov exponents of the chaotic saddle mean that we need to be very careful in interpreting numerical simulations where the return times become long; this can critically influence the simulation of phase-resetting and connection selection
On the zero set of G-equivariant maps
Let be a finite group acting on vector spaces and and consider a
smooth -equivariant mapping . This paper addresses the question of
the zero set near a zero of with isotropy subgroup . It is known
from results of Bierstone and Field on -transversality theory that the zero
set in a neighborhood of is a stratified set. The purpose of this paper is
to partially determine the structure of the stratified set near using only
information from the representations and . We define an index
for isotropy subgroups of which is the difference of
the dimension of the fixed point subspace of in and . Our main
result states that if contains a subspace -isomorphic to , then for
every maximal isotropy subgroup satisfying , the zero
set of near contains a smooth manifold of zeros with isotropy subgroup
of dimension . We also present a systematic method to study
the zero sets for group representations and which do not satisfy the
conditions of our main theorem. The paper contains many examples and raises
several questions concerning the computation of zero sets of equivariant maps.
These results have application to the bifurcation theory of -reversible
equivariant vector fields
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Neural processing of imminent collision in humans
Detecting a looming object and its imminent collision is imperative to survival. For most humans, it is a fundamental aspect of daily activities such as driving, road crossing and participating in sport, yet little is known about how the brain both detects and responds to such stimuli. Here we use functional magnetic resonance imaging to assess neural response to looming stimuli in comparison with receding stimuli and motion-controlled static stimuli. We demonstrate for the first time that, in the human, the superior colliculus and the pulvinar nucleus of the thalamus respond to looming in addition to cortical regions associated with motor preparation. We also implicate the anterior insula in making timing computations for collision events
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An fMRI study of parietal cortex involvement in the visual guidance of locomotion
Locomoting through the environment typically involves anticipating impending changes in heading trajectory in addition to maintaining the current direction of travel. We explored the neural systems involved in the “far road” and “near road” mechanisms proposed by Land and Horwood (1995) using simulated forward or backward travel where participants were required to gauge their current direction of travel (rather than directly control it). During forward egomotion, the distant road edges provided future path information, which participants used to improve their heading judgments. During backward egomotion, the road edges did not enhance performance because they no longer provided prospective information. This behavioral dissociation was reflected at the neural level, where only simulated forward travel increased activation in a region of the superior parietal lobe and the medial intraparietal sulcus. Providing only near road information during a forward heading judgment task resulted in activation in the motion complex. We propose a complementary role for the posterior parietal cortex and motion complex in detecting future path information and maintaining current lane positioning, respectively. (PsycINFO Database Record (c) 2010 APA, all rights reserved
Phenomenology of the Flavor-Asymmetry in the Light-Quark Sea of the Nucleon
A phenomenological ansatz for the flavor-asymmetry of the light sea
distributions of the nucleon, based on the Pauli exclusion principle, is
proposed. This ansatz is compatible with the measured flavor-asymmetry of the
unpolarized sea distributions, , of the nucleon. A prediction
for the corresponding polarized flavor-asymmetry is presented and shown to
agree with predictions of (chiral quark--soliton) models which successfully
reproduced the flavor-asymmetry of the unpolarized sea.Comment: 5 pages, LaTeX, 2 figures, uses epsfi
Bunge’s Mathematical Structuralism Is Not a Fiction
In this paper, I explore Bunge’s fictionism in philosophy of mathematics. After an overview of Bunge’s views, in particular his mathematical structuralism, I argue that the comparison between mathematical objects and fictions ultimately fails. I then sketch a different ontology for mathematics, based on Thomasson’s metaphysical work. I conclude that mathematics deserves its own ontology, and that, in the end, much work remains to be done to clarify the various forms of dependence that are involved in mathematical knowledge, in particular its dependence on mental/brain states and material objects
Polarization of Astronomical Maser Radiation. IV. Circular Polarization Profiles
Profile comparison of the Stokes parameters and is a powerful tool
for maser data analysis, providing the first direct methods for unambiguous
determination of (1) the maser saturation stage, (2) the amplification optical
depth and intrinsic Doppler width of unsaturated masers, and (3) the
comparative magnitudes of Zeeman splitting and Doppler linewidth. Circular
polarization recently detected in OH 1720 MHz emission from the Galactic center
appears to provide the first direct evidence for maser saturation.Comment: 14 pages, 1 Postscript figures (included), uses aaspp4.sty. To appear
in Astrophysical Journa
Derivation of the Lorentz Force Law, the Magnetic Field Concept and the Faraday-Lenz Law using an Invariant Formulation of the Lorentz Transformation
It is demonstrated how the right hand sides of the Lorentz Transformation
equations may be written, in a Lorentz invariant manner, as 4--vector scalar
products. This implies the existence of invariant length intervals analogous to
invariant proper time intervals. This formalism, making essential use of the
4-vector electromagnetic potential concept, provides a short derivation of the
Lorentz force law of classical electrodynamics, the conventional definition of
the magnetic field, in terms of spatial derivatives of the 4--vector potential
and the Faraday-Lenz Law. An important distinction between the physical
meanings of the space-time and energy-momentum 4--vectors is pointed out.Comment: 15 pages, no tables 1 figure. Revised and extended version of
physics/0307133 Some typos removed and minor text improvements in this
versio
Increased plasticity of the bodily self in eating disorders
Background: The rubber hand illusion (RHI) has been widely used to investigate the bodily self in healthy individuals. The aim of the present study was to extend the use of the RHI to examine the bodily self in eating disorders. Methods: The RHI and self-report measures of eating disorder psychopathology (EDI-3 subscales of Drive for Thinness, Bulimia, Body Dissatisfaction, Interoceptive Deficits, and Emotional Dysregulation; DASS-21; and the Self-Objectification Questionnaire) were administered to 78 individuals with an eating disorder and 61 healthy controls. Results: Individuals with an eating disorder experienced the RHI significantly more strongly than healthy controls on both perceptual (i.e., proprioceptive drift) and subjective (self-report questionnaire) measures. Furthermore, both the subjective experience of the RHI and associated proprioceptive biases were correlated with eating disorder psychopathology. Approximately 20% of the variance for embodiment of the fake hand was accounted for by eating disorder psychopathology, with interoceptive deficits and self-objectification significant predictors of embodiment. Conclusions: These results indicate that the bodily self is more plastic in people with an eating disorder. These findings may shed light on both aetiological and maintenance factors involved in eating disorders, particularly visual processing of the body, interoceptive deficits, and self-objectification
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