Search results for "Nonlinear"
showing 10 items of 3684 documents
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 …
Some remarks on nonlinear elliptic problems involving Hardy potentials
2007
In this note we prove an Hardy type inequality with a remainder term, where the potential depends only on a group of variables. Such a result allows us to show the existence of entropy solutions to a class of elliptic P.D.E.'s.
Pattern formation in hyperbolic reaction-transport systems and applications to dryland ecology
2023
Pattern formation and modulation is an active branch of mathematics, not only from the perspective of fundamental theory but also for its huge applications in many fields of physics, ecology, chemistry, biology, and other sciences. In this thesis, the occurrence of Turing and wave instabilities, giving rise to stationary and oscillatory patterns, respectively, is theoretically investigated by means of two-compartment reaction-transport hyperbolic systems. The goal is to elucidate the role of inertial times, which are introduced in hyperbolic models to account for the finite-time propagation of disturbances, in stationary and transient dynamics, in supercritical and subcritical regimes. In p…
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…
Conflicting legitimations and pressures in performance measurement adoption, use and change in Finnish municipalities
2010
Approximation of pre-twisted Achilles sub-tendons with continuum beam elements
2022
Achilles sub-tendons are materially and geometrically challenging structures that can nearly undergo around 15% elongation from their pre-twisted initial states during physical activities. Sub-tendons' cross-sectional shapes are subject-specific, varying from simple to complicated. Therefore, the Achilles sub-tendons are often described by three-dimensional elements that lead to a remarkable number of degrees of freedom. On the other hand, the continuum-based beam elements in the framework of the absolute nodal coordinate formulation have already been shown to be a reliable and efficient replacement for the three-dimensional continuum elements in some special problems. So far, that element …
Time-delay control for stabilization of the Shapovalov mid-size firm model
2020
Control and stabilization of irregular and unstable behavior of dynamic systems (including chaotic processes) are interdisciplinary problems of interest to a variety of scientific fields and applications. Using the control methods allows improvements in forecasting the dynamics of unstable economic processes and offers opportunities for governments, central banks, and other policy makers to modify the behaviour of the economic system to achieve its best performance. One effective method for control of chaos and computation of unstable periodic orbits (UPOs) is the unstable delay feedback control (UDFC) approach, suggested by K. Pyragas. This paper proposes the application of the Pyragas' me…
D3 Dihedral Logistic Map of Fractional Order
2021
In this paper, the D3 dihedral logistic map of fractional order is introduced. The map presents a dihedral symmetry D3. It is numerically shown that the construction and interpretation of the bifurcation diagram versus the fractional order requires special attention. The system stability is determined and the problem of hidden attractors is analyzed. Furthermore, analytical and numerical results show that the chaotic attractor of integer order, with D3 symmetries, looses its symmetry in the fractional-order variant.