Search results for "Nonlinear system"
showing 10 items of 1446 documents
Nonlinear optical spectra of conjugated polymers: Effect of long-range coulomb interactions
1993
Abstract Nonlinear optical spectra of conjugated polymers are theoretically studied in the Su-Schrieffer-Heeger model supplemented by long-range Coulomb interactions. Excitonic correlation for electron-hole excitations in explicitly taken into account by a standard method. Nonlinear susceptibilities χ (3) are calculated numerically with a standard sum-over-states method for finite chains (up to 1000 sites). Using moderate interaction strength, our calculations can reproduce many distinct features observed in the linear and nonlinear spectra (two-photon absorption, third-harmonic generation, and electroabsorption) of polydiacetylenes and some other polymers. Especially, a hump in the spectru…
Coherence resonance in Bonhoeffer-Van der Pol circuit
2009
International audience; A nonlinear electronic circuit simulating the neuronal activity in a noisy environment is proposed. This electronic circuit is exactly ruled by the set of Bonhoeffer-Van Der Pol equations and is excited with a Gaussian noise. Without external deterministic stimuli, it is shown that the circuit exhibits the so-called 'coherence resonance' phenomenon.
An output-only stochastic parametric approach for the identification of linear and nonlinear structures under random base excitations: Advances and c…
2014
In this paper a time domain output-only Dynamic Identification approach for Civil Structures (DICS) first formulated some years ago is reviewed and presented in a more generalized form. The approach in question, suitable for multi- and single-degrees-of-freedom systems, is based on the statistical moments and on the correlation functions of the response to base random excitations. The solving equations are obtained by applying the Itô differential stochastic calculus to some functions of the response. In the previous version ([21] Cavaleri, 2006; [22] Benfratello et al., 2009), the DICS method was based on the use of two classes of models (Restricted Potential Models and Linear Mass Proport…
State-feedback sampled-data control design for nonlinear systems via passive theory
2013
Published version of an article in the journal: Mathematical Problems in Engineering. Also available from the publisher at: http://dx.doi.org/10.1155/2013/230413 Open Access This paper investigates the problem of passive controller design for a class of nonlinear systems under variable sampling. The Takagi-Sugeno (T-S) fuzzy modeling method is utilized to represent the nonlinear systems. Attention is focused on the design of passive controller for the T-S fuzzy systems via sampled-data control approach. Under the concept of very-strict passivity, a novel time-dependent Lyapunov functional is constructed to develop passive analysis criteria and passive controller synthesis conditions. A new …
Oscillatory Behavior of Second-Order Nonlinear Neutral Differential Equations
2014
Published version of an article in the journal: Abstract and Applied Analysis. Also available from the publisher at: http://dx.doi.org/10.1155/2014/143614 Open Access We study oscillatory behavior of solutions to a class of second-order nonlinear neutral differential equations under the assumptions that allow applications to differential equations with delayed and advanced arguments. New theorems do not need several restrictive assumptions required in related results reported in the literature. Several examples are provided to show that the results obtained are sharp even for second-order ordinary differential equations and improve related contributions to the subject.
Stochastic Stability Analysis for Markovian Jump Neutral Nonlinear Systems
2012
In this paper, the stability problem is studied for a class of Markovian jump neutral nonlinear systems with time-varying delay. By Lyapunov-Krasovskii function approach, a novel mean-square exponential stability criterion is derived for the situations that the system's transition rates are completely accessible, partially accessible and non-accessible, respectively. Moreover, the developed stability criterion is extended to the systems with different bounded sector nonlinear constraints. Finally, some numerical examples are provided to illustrate the effectiveness of the proposed methods.
Approximating hidden chaotic attractors via parameter switching.
2018
In this paper, the problem of approximating hidden chaotic attractors of a general class of nonlinear systems is investigated. The parameter switching (PS) algorithm is utilized, which switches the control parameter within a given set of values with the initial value problem numerically solved. The PS-generated attractor approximates the attractor obtained by averaging the control parameter with the switched values, which represents the hidden chaotic attractor. The hidden chaotic attractors of a generalized Lorenz system and the Rabinovich-Fabrikant system are simulated for illustration. In Refs. 1–3, it is proved that the attractors of a chaotic system, considered as the unique numerical …
Solutions of nonlinear PDEs in the sense of averages
2012
Abstract We characterize p-harmonic functions including p = 1 and p = ∞ by using mean value properties extending classical results of Privaloff from the linear case p = 2 to all pʼs. We describe a class of random tug-of-war games whose value functions approach p-harmonic functions as the step goes to zero for the full range 1 p ∞ .
On the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations
2020
Abstract By using comparison principles, we analyze the asymptotic behavior of solutions to a class of third-order nonlinear neutral differential equations. Due to less restrictive assumptions on the coefficients of the equation and on the deviating argument τ , our criteria improve a number of related results reported in the literature.
A Multiplicity result for a class of strongly indefinite asymptotically linear second order systems
2010
We prove a multiplicity result for a class of strongly indefinite nonlinear second order asymptotically linear systems with Dirichlet boundary conditions. The key idea for the proof is to bring together the classical shooting method and the Maslov index of the linear Hamiltonian systems associated to the asymptotic limits of the given nonlinearity.