Search results for "nonlinear"
showing 10 items of 3684 documents
Symbolic control for underactuated differentially flat systems
2006
In this paper we address the problem of generating input plans to steer complex dynamical systems in an obstacle-free environment. Plans considered admit a finite description length and are constructed by words on an alphabet of input symbols, which could be e.g. transmitted through a limited capacity channel to a remote system, where they can be decoded in suitable control actions. We show that, by suitable choice of the control encoding, finite plans can be efficiently built for a wide class of dynamical systems, computing arbitrarily close approximations of a desired equilibrium in polynomial time. Moreover, we illustrate by simulations the power of the proposed method, solving the steer…
Exchange rates expectations and chaotic dynamics: a replication study
2018
Abstract In this paper the author analyzes the behavior of exchange rates expectations for four currencies, by considering a re-calculation and an extension of Resende and Zeidan (Expectations and chaotic dynamics: empirical evidence on exchange rates, Economics Letters, 2008). Considering Lyapunov exponent-based tests results, they are not supportive of chaos in exchange rates expectations, although the so-called 0–1 test strongly supports the chaos hypothesis.
Analysis of neuronal networks in the visual system of the cat using statistical signals
1976
If the input signals of the visual system in the cat are statistical patterns in space and time, a complete system analysis can be carried out. What counts here as a system are the neuronal networks between retina and recording site. In the case of linearity, one obtains the temporal impulse response functions at every point in the receptive field with the aid of correlation methods. The measuring time is about one minute. Some aspects of the procedure are explained in terms of examples. The method of measurement also makes it possible to determine the characteristic function of the system in time and space between different recording sites within the cortex. It is possible to specialize th…
On the use of fractional calculus for the probabilistic characterization of random variables
2009
In this paper, the classical problem of the probabilistic characterization of a random variable is re-examined. A random variable is usually described by the probability density function (PDF) or by its Fourier transform, namely the characteristic function (CF). The CF can be further expressed by a Taylor series involving the moments of the random variable. However, in some circumstances, the moments do not exist and the Taylor expansion of the CF is useless. This happens for example in the case of $\alpha$--stable random variables. Here, the problem of representing the CF or the PDF of random variables (r.vs) is examined by introducing fractional calculus. Two very remarkable results are o…
Path integral solution for non-linear system enforced by Poisson White Noise
2008
Abstract In this paper the response in terms of probability density function of non-linear systems under Poisson White Noise is considered. The problem is handled via path integral (PI) solution that may be considered as a step-by-step solution technique in terms of probability density function. First the extension of the PI to the case of Poisson White Noise is derived, then it is shown that at the limit when the time step becomes an infinitesimal quantity the Kolmogorov–Feller (K–F) equation is fully restored enforcing the validity of the approximations made in obtaining the conditional probability appearing in the Chapman Kolmogorov equation (starting point of the PI). Spectral counterpa…
A method for the probabilistic analysis of nonlinear systems
1995
Abstract The probabilistic description of the response of a nonlinear system driven by stochastic processes is usually treated by means of evaluation of statistical moments and cumulants of the response. A different kind of approach, by means of new quantities here called Taylor moments, is proposed. The latter are the coefficients of the Taylor expansion of the probability density function and the moments of the characteristic function too. Dual quantities with respect to the statistical cumulants, here called Taylor cumulants, are also introduced. Along with the basic scheme of the method some illustrative examples are analysed in detail. The examples show that the proposed method is an a…
Probabilistic response of nonlinear systems under combined normal and Poisson white noise via path integral method
2011
In this paper the response in terms of probability density function of nonlinear systems under combined normal and Poisson white noise is considered. The problem is handled via a Path Integral Solution (PIS) that may be considered as a step-by-step solution technique in terms of probability density function. A nonlinear system under normal white noise, Poissonian white noise and under the superposition of normal and Poisson white noise is performed through PIS. The spectral counterpart of the PIS, ruling the evolution of the characteristic functions is also derived. It is shown that at the limit when the time step becomes an infinitesimal quantity an equation ruling the evolution of the pro…
Application of Genetic Algorithm on Parameter Optimization of Three Vehicle Crash Scenarios
2017
Abstract This paper focuses on the development of mathematical models for vehicle frontal crashes. The models under consideration are threefold: a vehicle into barrier, vehicle-occupant and vehicle to vehicle frontal crashes. The first model is represented as a simple spring-mass-damper and the second case consists of a double-spring-mass-damper system, whereby the front mass and the rear mass represent the vehicle chassis and the occupant, respectively. The third model consists of a collision of two vehicles represented by two masses moving in opposite directions. The springs and dampers in the models are nonlinear piecewise functions of displacements and velocities respectively. More spec…
A new monomeric interpretation of intrinsic optical bistability observed in Yb3+-doped bromide materials
2003
We present a mechanism able to show intrinsic bistable behaviour involving single Yb3+ ions embedded into bromide lattices, in which intrinsic optical bistability (IOB) has been observed. The mechanism is based on the experimentally found coupling between the Yb3+ ion and the totally symmetric local mode of vibration of the [YbBr6]3- coordination unit. The model reproduces the IOB observed in CsCdBr3:1% Yb3+ and allows to understand the experimentally found presence of the phenomenon in the other bromides, but its absence in Cs3Lu2Cl9:Yb3+.
Generalized transport coefficients in a gas with large shear rate
1987
We get a solution of the Bhatnagar-Gross-Krook (BGK) model kinetic equation by means of a perturbative expansion of a temperature gradient to study the transport properties in a gas with large shear rate. The irreversible fluxes are evaluated exactly to first order in the expansion for Maxwell molecules. The transport coefficients obtained are highly nonlinear functions of the shear rate. This dependence on shear rate is analysed and compared with previous results for several transport coefficients. Finally, we have found a solution for a simple model of constant collision frequency for which a large shear rate coexists with an arbitrary temperature gradient.