Search results for "linear system"
showing 10 items of 1558 documents
A note on some fundamental results in complete gauge spaces and application
2015
We discuss the extension of some fundamental results in nonlinear analysis to the setting of gauge spaces. In particular, we establish Ekeland type and Caristi type results under suitable hypotheses for mappings and cyclic mappings. Our theorems generalize and complement some analogous results in the literature, also in the sense of ordered sets and oriented graphs. We apply our results to establishing the existence of solution to a second order nonlinear initial value problem.
Nonlinear nystagmus processing causes torsional VOR nonlinearity.
2003
The eye movement component that rotates around the line of sight, i.e., the ocular torsion, is in many aspects different from horizontal and vertical eye movements. While ocular torsion is mediated only by reflexive pathways like the torsional vestibulo-ocular and optokinetic reflexes (TVOR and OKN, respectively), horizontal and vertical components are also subject to intentional control mechanisms that are mediated by the saccadic and the pursuit systems. Dynamic properties of torsional eye movements are also very distinct. While horizontal and vertical VOR components show a gain close to unity and a small neural integration leakage with a time constant around pi=30 s, the TVOR shows a sma…
2020
In this paper a comprehensive system-level computational model of oculomotor pathways is presented. This model shows the necessity of embedding internal models of muscles biomechanics in the cerebellar Vermis to realize fast saccadic eye movements based on predicting the changes in muscles lengths. First, the eye biomechanics are described by nonlinear equations during “slow” and “fast” movements. Afterward, by analyzing these equations, a computational model, is deduced. Furthermore, each part of this model is interpreted as a possible function of an element in the oculomotor pathways based on physiological and anatomical pieces of evidence. In this model, two internal feedback loops compe…
Multiple positive normalized solutions for nonlinear Schrödinger systems
2018
We consider the existence of multiple positive solutions to the nonlinear Schr\"odinger systems sets on $H^1(\mathbb{R}^N) \times H^1(\mathbb{R}^N)$, \[ \left\{ \begin{aligned} -\Delta u_1 &= \lambda_1 u_1 + \mu_1 |u_1|^{p_1 -2}u_1 + \beta r_1 |u_1|^{r_1-2} u_1|u_2|^{r_2}, -\Delta u_2 &= \lambda_2 u_2 + \mu_2 |u_2|^{p_2 -2}u_2 + \beta r_2 |u_1|^{r_1} |u_2|^{r_2 -2} u_2, \end{aligned} \right. \] under the constraint \[ \int_{\mathbb{R}^N}|u_1|^2 \, dx = a_1,\quad \int_{\mathbb{R}^N}|u_2|^2 \, dx = a_2. \] Here $a_1, a_2 >0$ are prescribed, $\mu_1, \mu_2, \beta>0$, and the frequencies $\lambda_1, \lambda_2$ are unknown and will appear as Lagrange multipliers. Two cases are studied, the first …
Spectral dynamics of incoherent waves with a noninstantaneous nonlinear response
2013
We study the influence of a constant background noise on the dynamics of spectral incoherent solitons, which are incoherent structures sustained by a noninstantaneous (Raman-like) nonlinearity. As the level of the noise background increases, the incoherent wave enters a novel nonlinear regime characterized by oscillatory dynamics of the incoherent spectrum, which develop within a spectral cone during the propagation. In contrast to the conventional Raman-like spectral red shift, such incoherent spectral dynamics can be characterized by a significant spectral blue shift. On the basis of the kinetic wave theory, we derive explicit analytical expressions of these incoherent oscillatory spectra…
Feedback Linearizing Control of Induction Motor Considering Magnetic Saturation Effects
2015
This paper presents an input-output feedback linearization (FL) control technique for rotating induction motors, which takes into consideration the magnetic saturation of the iron core. Starting from a new formulation of the dynamic model taking into consideration the magnetic saturation expressed in a space-state form in the rotor-flux-oriented reference frame, the corresponding FL technique has been developed. To this aim, a particular care has been given to the choice of nonlinear functions interpolating the magnetic parameters versus the rotor magnetizing current and the corresponding magnetic characteristic. The proposed FL technique has been tested experimentally on a suitably develop…
Nonlinear Disorder Mapping Through Three-Wave Mixing
2010
We implement a simple and powerful approach to characterize the domain distribution in the bulk of quadratic ferroelectric crystals via far-field second-harmonic spectroscopy. The approach is demonstrated in a lithium tantalate sample with periodic electric field poling and random mark-to-space ratio.
System identification via optimised wavelet-based neural networks
2003
Nonlinear system identification by means of wavelet-based neural networks (WBNNs) is presented. An iterative method is proposed, based on a way of combining genetic algorithms (GAs) and least-square techniques with the aim of avoiding redundancy in the representation of the function. GAs are used for optimal selection of the structure of the WBNN and the parameters of the transfer function of its neurones. Least-square techniques are used to update the weights of the net. The basic criterion of the method is the addition of a new neurone, at a generic step, to the already constructed WBNN so that no modification to the parameters of its neurones is required. Simulation experiments and compa…
On a Robin (p,q)-equation with a logistic reaction
2019
We consider a nonlinear nonhomogeneous Robin equation driven by the sum of a \(p\)-Laplacian and of a \(q\)-Laplacian (\((p,q)\)-equation) plus an indefinite potential term and a parametric reaction of logistic type (superdiffusive case). We prove a bifurcation-type result describing the changes in the set of positive solutions as the parameter \(\lambda \gt 0\) varies. Also, we show that for every admissible parameter \(\lambda \gt 0\), the problem admits a smallest positive solution.
Information-theoretic assessment of cardiovascular-brain networks during sleep
2015
This study was aimed at detecting the structure of the physiological network underlying the regulation of the cardiovascular and brain systems during normal sleep. To this end, we measured from the polysomnographic recordings of 10 healthy subjects the normalized spectral power of heart rate variability in the high frequency band (HF) and the EEG power in the δ, θ, α, σ, and β bands. Then, the causal statistical dependencies within and between these six time series were assessed in terms of internal information (conditional self entropy, CSE) and information transfer (transfer entropy, TE) computed via a linear method exploiting multiple regression models and a nonlinear method combining ne…