32,690 research outputs found
Minimum Restraint Functions for unbounded dynamics: general and control-polynomial systems
We consider an exit-time minimum problem with a running cost, and
unbounded controls. The occurrence of points where can be regarded as a
transversality loss. Furthermore, since controls range over unbounded sets, the
family of admissible trajectories may lack important compactness properties. In
the first part of the paper we show that the existence of a -minimum
restraint function provides not only global asymptotic controllability (despite
non-transversality) but also a state-dependent upper bound for the value
function (provided ). This extends to unbounded dynamics a former result
which heavily relied on the compactness of the control set.
In the second part of the paper we apply the general result to the case when
the system is polynomial in the control variable. Some elementary, algebraic,
properties of the convex hull of vector-valued polynomials' ranges allow some
simplifications of the main result, in terms of either near-affine-control
systems or reduction to weak subsystems for the original dynamics.Comment: arXiv admin note: text overlap with arXiv:1503.0344
Dissipative chaotic scattering
We show that weak dissipation, typical in realistic situations, can have a
metamorphic consequence on nonhyperbolic chaotic scattering in the sense that
the physically important particle-decay law is altered, no matter how small the
amount of dissipation. As a result, the previous conclusion about the unity of
the fractal dimension of the set of singularities in scattering functions, a
major claim about nonhyperbolic chaotic scattering, may not be observable.Comment: 4 pages, 2 figures, revte
Fluctuations of Entropy Production in Partially Masked Electric Circuits: Theoretical Analysis
In this work we perform theoretical analysis about a coupled RC circuit with
constant driven currents. Starting from stochastic differential equations,
where voltages are subject to thermal noises, we derive time-correlation
functions, steady-state distributions and transition probabilities of the
system. The validity of the fluctuation theorem (FT) is examined for scenarios
with complete and incomplete descriptions.Comment: 4 pages, 1 figur
Neuroplastic Changes Following Brain Ischemia and their Contribution to Stroke Recovery: Novel Approaches in Neurorehabilitation
Ischemic damage to the brain triggers substantial reorganization of spared areas and pathways, which is associated with limited, spontaneous restoration of function. A better understanding of this plastic remodeling is crucial to develop more effective strategies for stroke rehabilitation. In this review article, we discuss advances in the comprehension of post-stroke network reorganization in patients and animal models. We first focus on rodent studies that have shed light on the mechanisms underlying neuronal remodeling in the perilesional area and contralesional hemisphere after motor cortex infarcts. Analysis of electrophysiological data has demonstrated brain-wide alterations in functional connectivity in both hemispheres, well beyond the infarcted area. We then illustrate the potential use of non-invasive brain stimulation (NIBS) techniques to boost recovery. We finally discuss rehabilitative protocols based on robotic devices as a tool to promote endogenous plasticity and functional restoration
Strange nonchaotic attractors in noise driven systems
Strange nonchaotic attractors (SNAs) in noise driven systems are
investigated. Before the transition to chaos, due to the effect of noise, a
typical trajectory will wander between the periodic attractor and its nearby
chaotic saddle in an intermittent way, forms a strange attractor gradually. The
existence of SNAs is confirmed by simulation results of various critera both in
map and continuous systems. Dimension transition is found and intermittent
behavior is studied by peoperties of local Lyapunov exponent. The universality
and generalization of this kind of SNAs are discussed and common features are
concluded
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