Search results for "Linear system"
showing 10 items of 1558 documents
Compound conditionals, Fr\'echet-Hoeffding bounds, and Frank t-norms
2021
Abstract In this paper we consider compound conditionals, Frechet-Hoeffding bounds and the probabilistic interpretation of Frank t-norms. By studying the solvability of suitable linear systems, we show under logical independence the sharpness of the Frechet-Hoeffding bounds for the prevision of conjunctions and disjunctions of n conditional events. In addition, we illustrate some details in the case of three conditional events. We study the set of all coherent prevision assessments on a family containing n conditional events and their conjunction, by verifying that it is convex. We discuss the case where the prevision of conjunctions is assessed by Lukasiewicz t-norms and we give explicit s…
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…
A Mellin transform approach to wavelet analysis
2015
The paper proposes a fractional calculus approach to continuous wavelet analysis. Upon introducing a Mellin transform expression of the mother wavelet, it is shown that the wavelet transform of an arbitrary function f(t) can be given a fractional representation involving a suitable number of Riesz integrals of f(t), and corresponding fractional moments of the mother wavelet. This result serves as a basis for an original approach to wavelet analysis of linear systems under arbitrary excitations. In particular, using the proposed fractional representation for the wavelet transform of the excitation, it is found that the wavelet transform of the response can readily be computed by a Mellin tra…
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.
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.…
Nonlinear dynamics of a two-photon Fabry–Pérot laser
2000
Abstract The steady-state emission, stability and temporal dynamics of a single-mode two-photon laser with a Fabry–Perot cavity is investigated and compared with that of a ring-cavity laser. It is found that the Fabry–Perot cavity makes the laser less efficient than the ring cavity because of spatial hole burning, but the domain of stability is larger for the Fabry–Perot laser. The intensity and phase dynamics are numerically investigated and distinctive features are found in the phase dynamics as compared with one-photon lasers.
Robust stabilisation of 2D state-delayed stochastic systems with randomly occurring uncertainties and nonlinearities
2013
This paper is concerned with the state feedback control problem for a class of two-dimensional (2D) discrete-time stochastic systems with time-delays, randomly occurring uncertainties and nonlinearities. Both the sector-like nonlinearities and the norm-bounded uncertainties enter into the system in random ways, and such randomly occurring uncertainties and nonlinearities obey certain mutually uncorrelated Bernoulli random binary distribution laws. Sufficient computationally tractable linear matrix inequality–based conditions are established for the 2D nonlinear stochastic time-delay systems to be asymptotically stable in the mean-square sense, and then the explicit expression of the desired…
On multiples of divisors associated to Veronese embeddings with defective secant variety
2009
In this note we consider multiples aD, where D is a divisor of the blow-up of P^n along points in general position which appears in the Alexander and Hirschowitz list of Veronese embeddings having defective secant varieties. In particular we show that there is such a D with h^1(X,D) > 0 and h^1(X,2D) = 0.
Stabilization of a class of slowly switched positive linear systems: State-feedback control
2012
The main goal of this paper is to investigate the stabilization problem for a class of switched positive linear systems (SPLS) with average dwell time (ADT) switching in continuous-time context. State-feedback controllers and the corresponding switching law with ADT property are designed, which stabilize the closed-loop systems while keeping the states nonnegative. The proposed conditions, formulated as linear matrix inequalities, can be directly used for controller synthesis and switching designing. Finally, a numerical example is given to demonstrate the validity of the obtained results.