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showing 10 items of 4526 documents
Probabilistic response of linear structures equipped with nonlinear damper devices (PIS method)
2008
Passive control introducing energy absorbing devices into the structure has received considerable attention in recent years. Unfortunately the constitutive law of viscous fluid dampers is highly nonlinear, and even supposing that the structure behaves linearly, the whole system has inherent nonlinear properties. Usually the analysis is performed by a stochastic linearization technique (SLT) determining a linear system equivalent to the nonlinear one, in a statistical sense. In this paper the effect of the non-Gaussianity of the response due to the inherent nonlinearity of the damper device will be studied in detail via the Path Integral Solution (PIS) method. A systematic study is conducted…
Statistics of residence time for Lévy flights in unstable parabolic potentials
2020
We analyze the residence time problem for an arbitrary Markovian process describing nonlinear systems without a steady state. We obtain exact analytical results for the statistical characteristics of the residence time. For diffusion in a fully unstable potential profile in the presence of Lévy noise we get the conditional probability density of the particle position and the average residence time. The noise-enhanced stability phenomenon is observed in the system investigated. Results from numerical simulations are in very good agreement with analytical ones.
Effective target arrangement in a deterministic scale-free graph
2010
We study the random walk problem on a deterministic scale-free network, in the presence of a set of static, identical targets; due to the strong inhomogeneity of the underlying structure the mean first-passage time (MFPT), meant as a measure of transport efficiency, is expected to depend sensitively on the position of targets. We consider several spatial arrangements for targets and we calculate, mainly rigorously, the related MFPT, where the average is taken over all possible starting points and over all possible paths. For all the cases studied, the MFPT asymptotically scales like N^{theta}, being N the volume of the substrate and theta ranging from (1 - log 2/log3), for central target(s)…
Experimental and numerical study of noise effects in a FitzHugh-Nagumo system driven by a biharmonic signal
2013
Using a nonlinear circuit ruled by the FitzHugh-Nagumo equations, we experimentally investigate the combined effect of noise and a biharmonic driving of respective high and low frequency F and f. Without noise, we show that the response of the circuit to the low frequency can be maximized for a critical amplitude B of the high frequency via the effect of Vibrational Resonance (V.R.). We report that under certain conditions on the biharmonic stimulus, white noise can induce V.R. The effects of colored noise on V.R. are also discussed by considering an Ornstein-Uhlenbeck process. All experimental results are confirmed by numerical analysis of the system response.
Stochastic acceleration in generalized squared Bessel processes
2015
We analyze the time behavior of generalized squared Bessel processes, which are useful for modeling the relevant scales of stochastic acceleration problems. These nonstationary stochastic processes obey a Langevin equation with a non-Gaussian multiplicative noise. We obtain the long-time asymptotic behavior of the probability density function for non-Gaussian white and colored noise sources. We find that the functional form of the probability density functions is independent of the statistics of the noise source considered. Theoretical results are in good agreement with those obtained by numerical simulations of the Langevin equation with pulse noise sources.
On stability and dissipativity of stochastic nonlinear systems
2012
Input-to-state stability of nonlinear control system is described in several different manners, and has been a central concept since the equivalences among them were verified. In this paper, a framework of stability and dissipativity for stochastic control systems is constructed on the maximal existence interval of behaviors (states and external inputs), by the aid of stochastic Barbalat lemma and stochastic dissipativity. The main work consists of three aspects. First, input-to-state stability and robust stability are extended to the stochastic case, and several criteria are established. Second, two forms of dissipativity and their criteria are presented. Third, the key relations among the…
Ito and Stratonovich integrals for delta-correlated processes
1993
Abstract In this paper the generalization of the Itd and Stratonovich integrals for the case of non-linear systems excited by parametric delta-correlated processes is presented. This generalization gives a new light on the corrective coefficients in the stochastic differential equations driven by parametric delta-correlated processes. The full significance of these corrective terms is evidenced by means of some examples.
A subtle error in conventional stochastic linearization techniques
1998
Abstract The stochastic linearization technique as applied to the SDOF system is re-examined. Two standard procedures associated with the stochastic linearization, widely adopted in the literature, are shown to be erroneous. Two new procedures to correct the errors made in previous works are introduced. To gain more insight, the procedures are applied to the quintic oscillator. Comparative numerical analysis is performed.
Stochastic integro-differential and differential equations of non-linear systems excited by parametric Poisson pulses
1997
Abstract The connection between stochastic integro-differential equation and stochastic differential equation of non-linear systems driven by parametric Poisson delta correlated processes is presented. It is shown that the two different formulations are fully equivalent in the case of external excitation. In the case of parametric type excitation the two formulation are equivalent if the non-linear argument in the integral representation is related by means of a series to the corresponding non-linear parametric term in the stochastic differential equation. Differential rules for the two representations to find moment equations of every order of the response are also compared.
Einstein-Smoluchowsky equation handled by complex fractional moments
2014
In this paper the response of a non linear half oscillator driven by α-stable white noise in terms of probability density function (PDF) is investigated. The evolution of the PDF of such a system is ruled by the so called Einstein-Smoluchowsky equation involving, in the diffusive term, the Riesz fractional derivative. The solution is obtained by the use of complex fractional moments of the PDF, calculated with the aid of Mellin transform operator. It is shown that solution can be found for various values of stability index α and for any nonlinear function of the drift term in the stochastic differential equation.