arXiv subjects
Publications and source records attributed to Erivelton G. Nepomuceno.
This article investigates the maximum time of simulation in which the phenomenon of the intermittence can be observed with numerical confidence in discrete maps. Interval analysis and the lower error limit were used. As a result, it was observed that the reliability of the intermittency is dependent on the initial condition. Four numerical examples show the efficiency of the proposal.
Numerical problems are considered on general synchronization of chaotic oscillators, through the evaluation of the Lower Bound Error index on two case studies: a Lorenz system unidirectionally coupled to a Duffing system and a Duffing system unidirectionally coupled to a Rossler system. It was possible to observe, in each case, that the behavior of the slave's LBE curve tends to follow the behavior of the master's as the value of the coupling constant is increased up to a certain value, and thus, that synchronization can affect numerical calculations.
An improvement on precision of recursive function simulation in IEEE floating point standard is presented. It is shown that the average of rounding towards negative infinite and rounding towards positive infinite yields a better result than the usual standard rounding to the nearest in the simulation of recursive functions. In general, the method improves one digit of precision and it has also been useful to avoid divergence from a correct stationary regime in the logistic map. Numerical studies are presented to illustrate the method.
This paper presents an analysis on the effects of floating-point arithmetic on the constructing bifurcation diagram of the quadratic map. More precisely, we are interested in showing the dependence of initial conditions to obtain some specific features of the diagram. With this study, it was possible to observe that when there is a restriction regarding the initial condition, the results present aspects with significant differences of the ones found in the literature regarding the behaviour of the map, consequently there is a considerable modification in its bifurcation diagram. We show that these difference are related to floating-point arithmetic
This work deals with chaos suppression based on average of the rounded modes to negative and positive infinite. The present procedure acts to reduce the rounding errors. It was observed that when the method proposed in this paper is applied to the chaotic Lorenz's system, it exhibits a periodic behaviour, characterized by a limit cycle and negative largest Lyapunov exponent. We tested our approach using three discretization schemes based on Runge-Kutta method
This paper proposes a model validation method that incorporates error due to numerical procedures. Two identified models for Sine Map and Duffing-Ueda Circuit systems have been investigated. The indexes RMSE and MAPE have been applied. We have shown that after some few iterates, it is possible to notice some significative difference between index provided in the literature. This difference has been computed in around 34%.
The Lyapunov exponent is used to characterize the stability of the dynamic response of the system, and it is often employed to verify if a system is chaotic. Since its discovery in the nineteenth century, various methods have been proposed and developed for its calculation. The present work proposes a method for the calculation of the largest Lyapunov exponent, based on conditional number of the function, which describes the loss of bits in the simulation based on relative rounding error. Four discrete maps are used to show the effectiveness of the proposed method.
In this work the non-linear and chaotic behaviour for the RLD circuit is analysed, which is modelled by state space and numerically simulated considering the diode model an association between nonlinear resistances and capacitances. It has been possible to characterize the dynamics of the circuit through period doubles and chaotic behaviour. The Lyapunov exponent is calculated to show the chaotic behaviour of this circuit. Simulated results are in good agreement with experimental data.
This article presents a design of the logistic map by means of FPGA (Field Programmable Gate Ar-ray) under fixed-point standard and 32-bits of precision. The design was carried out with Altera Quartus platform. The hardware description language VHDL-93 has been adopted and the results were simulated by means of Altera ModelSim package. The main of the project was to produce a cha-otic system with a low energy and time cost. Using the VHDL, it was possible to use only 1439 logical gates from 114480 available. The Lyapunov exponent has been calculated with good agreement with literature reference, which shows the effectiveness the proposed method.
This paper aims to identify three electrical systems: a series RLC circuit, a motor/generator coupled system, and the Duffing-Ueda oscillator. In order to obtain the system's models was used the error reduction ratio and the Akaike information criterion. Our approach to handle the numerical errors was the interval arithmetic by means of the resolution of the least squares estimation. The routines was implemented in Intlab, a Matlab toolbox devoted to arithmetic interval. Finally, the interval RMSE was calculated to verify the quality of the obtained models. The applied methodology was satisfactory, since the obtained intervals encompass the system's data and allow to demonstrate how the numerical errors affect the answers.