Search results for "Stability."
showing 10 items of 3015 documents
Property (gab) through localized SVEP
2015
In this article we study the property (gab) for a bounded linear operator T 2 L(X) on a Banach space X which is a stronger variant of Browder's theorem. We shall give several characterizations of property (gab). These characterizations are obtained by using typical tools from local spectral theory. We also show that property (gab) holds for large classes of operators and prove the stability of property (gab) under some commuting perturbations. 2010 Mathematics Subject Classication. Primary 47A10, 47A11; Secondary 47A53, 47A55.
Periodic and Chaotic Orbits of a Neuron Model
2015
In this paper we study a class of difference equations which describes a discrete version of a single neuron model. We consider a generalization of the original McCulloch-Pitts model that has two thresholds. Periodic orbits are investigated accordingly to the different range of parameters. For some parameters sufficient conditions for periodic orbits of arbitrary periods have been obtained. We conclude that there exist values of parameters such that the function in the model has chaotic orbits. Models with chaotic orbits are not predictable in long-term.
Transitive partially hyperbolic diffeomorphisms on 3-manifolds
2005
Abstract The known examples of transitive partially hyperbolic diffeomorphisms on 3-manifolds belong to 3 basic classes: perturbations of skew products over an Anosov map of T 2 , perturbations of the time one map of a transitive Anosov flow, and certain derived from Anosov diffeomorphisms of the torus T 3 . In this work we characterize the two first types by a local hypothesis associated to one closed periodic curve.
Energy localization in a nonlinear discrete system
1996
International audience; We show that, in the weak amplitude and slow time limits, the discrete equations describing the dynamics of a one-dimensional lattice can be reduced to a modified Ablowitz-Ladik equation. The stability of a continuous wave solution is then investigated without and with periodic boundary conditions; Energy localization via modulational instability is predicted. Our numerical simulations, performed on a cyclic system of six oscillators, agree with our theoretical predictions.
Modulational instability and two-dimensional dynamical structures
2008
A process of nonlinear structure formation on a two-dimensional lattice is proposed. The basic model consists of a two-dimensional lattice equipped at each node with a molecule or dipole rotating in the lattice plane. The interactions involved in the model are reduced to a periodic lattice. Such a discrete system can be applied to the problem of molecule adsorption on a substrate crystal surface, for instance. The continuum approximation of the model leads to a 2-D sine-Gordon system including nonlinear couplings, which itself can be reduced to a 2-D nonlinear Schrodinger equation in the low amplitude limit. Spatio-temporal structure formation is investigated by means of numerical simulatio…
Quantum Relaxation Time in Asymmetric Bistable Potential
2010
Quantum tunneling effect occurs often in condensed matter physics, examples are JJs, heteronanostructures, etc.. The tunneling effect plays an important role in the nonlinear relaxation time from a metastable state in an open quantum system, interacting with a thermal bath. Symmetrical and asymmetric bistable systems are good quantum model systems for analysis of the "superconducting quantum bits" and decoherence phenomena. To obtain very long coherence times in the presence of interaction between the qubit and the noisy environment is one of the greatest challenges of physics. The inf1uence of the environment in quantum tunneling has been in the focus of intense research over the last year…
High Order Compact Finite Difference Schemes for A Nonlinear Black-Scholes Equation
2001
A nonlinear Black-Scholes equation which models transaction costs arising in the hedging of portfolios is discretized semi-implicitly using high order compact finite difference schemes. A new compact scheme, generalizing the compact schemes of Rigal [29], is derived and proved to be unconditionally stable and non-oscillatory. The numerical results are compared to standard finite difference schemes. It turns out that the compact schemes have very satisfying stability and non-oscillatory properties and are generally more efficient than the considered classical schemes.
ADI schemes for valuing European options under the Bates model
2018
Abstract This paper is concerned with the adaptation of alternating direction implicit (ADI) time discretization schemes for the numerical solution of partial integro-differential equations (PIDEs) with application to the Bates model in finance. Three different adaptations are formulated and their (von Neumann) stability is analyzed. Ample numerical experiments are provided for the Bates PIDE, illustrating the actual stability and convergence behaviour of the three adaptations.
Dissipative rogue wave generation in multiple-pulsing mode-locked fiber laser
2013
Following the first experimental observation of a new mechanism leading to optical rogue wave (RW) formation briefly reported in Lecaplain et al (2012 Phys. Rev. Lett. 108 233901), we provide an extensive study of the experimental conditions under which these RWs can be detected. RWs originate from the nonlinear interactions of bunched chaotic pulses that propagate in a fiber laser cavity, and manifest as rare events of high optical intensity. The crucial influence of the electrical detection bandwidth is illustrated. We also clarify the observation of RWs with respect to other pulsating regimes, such as Q-switching instability, that also lead to L-shaped probability distribution functions.…
Immediate implants following tooth extraction. A systematic review
2012
Objectives: The aim of this article is to review the current state of immediate implants, with their pros and contras, and the clinical indications and contraindications. Material and Methods: An exhaustive literature search has been carried out in the COCHRANE library and MEDLINE electronic databases from 2004 to November 2009. Randomized clinical trials and clinical trials focused on single implants placed in fresh extraction sockets were included and compared. A meta-analysis could not be performed due to heterogeneity of the data. Results: Twenty studies out of 135 articles from the initial search were finally included, which summed up a total of 1139 immediate implants with at least a …