An evergreen scientific feature is the ability for scientific works to be reproduced. Since chaotic systems are so hard to understand analytically, numerical simulations assume a key role in their investigation. Such simulations have been considered as reproducible in many works. However, few studies have focused on the effects of the finite precision of computers on the simulation reproducibility of chaotic systems; moreover, code sharing and details on how to reproduce simulation results are not present in many investigations. In this work, a case study of reproducibility is presented in the simulation of a chaotic jerk circuit, using the software LTspice. We also employ the OSF platform to share the project associated with this paper. Tests performed with LTspice XVII on four different computers show the difficulties of simulation reproducibility by this software. We compare these results with experimental data using a normalised root mean square error in order to identify the computer with the highest prediction horizon. We also calculate the entropy of the signals to check differences among computer simulations and the practical experiment. The methodology developed is efficient in identifying the computer with better performance, which allows applying it to other cases in the literature. This investigation is fully described and available on the OSF platform.
The number of researches aimed at understanding the chaotic behavior of nonlinear dynamical systems has grown considerably in recent years. The development of electronic circuits that exhibit this type of behavior has been the interest of numerous works in the literature. Among the possible sets of nonlinear systems, the simplest in which one can observe bifurcation phenomena and chaotic behavior, followed by wellcontrolled experiments, are nonlinear electronic circuits. One of the most widely used tools for analysis and evaluation of chaotic behavior is known as the bifurcation diagram. Generally, in the analysis of these circuits, parameters such as voltage, current and frequency are used to verify their respective behaviors. Variable values of passive components such as resistors and capacitors are also widely used. The temperature has also been used as a bifurcation parameter in resistor, diode and inductor (RLD) circuits. However, there is little attention from the scientific community on temperature as a bifurcation parameter for electronic circuits using operational amplifiers such as the chaotic Jerk circuit. In this sense, this project aims to implement a chaotic Jerk circuit, composed of operational amplifiers, resistors and capacitors, and subject it to different temperature levels, using this variable as an analysis parameter. Thus, at the end of this work it was possible to verify that the temperature variation directly influences the behavior of the investigated system, thus reaching the final objective of the project, presenting that the temperature can be a bifurcation parameter for a chaotic Jerk circuit.
This paper addresses the effect of isolation on the spread of Covid-19 in the State of Minas Gerais, Brazil. The compartmental model SEIR (Susceptible, Exposed, Infectious, Recovered) has been employed. The parameters of the model have been estimated with the help of optimization techniques based on evolutionary strategies. From the model obtained, this work evaluates the impacts of reducing the isolation in the peak of infected people. Results show that the isolation has reduced the peak in 94%, which has played a crucial role in avoiding the health system collapse up to now. Moreover, around 70% of isolation guarantees a good quality of health system service to deal with the pandemic of Covid-19 according to the number of intensive care units and considering a reproductive number equals to 3.60. This is an important result to be considered during easing physical distancing measures.
An evergreen scientific feature is the ability for scientific works to be reproduced. This feature allows researchers to understand, enhance, or even question works that have been developed by other scientists. In control theory the importance of modeling and simulation of systems is widely recognized. Despite this recognition, less attention is paid to the effects of finite precision of computers on the simulation reproducibility of nonlinear dynamic systems. In this work, a case study of reproducibility is presented in the simulation of a chaotic Jerk circuit, using the software LtSpice. In order to do so, we performed simulations of the circuit in the same version of the software on different computers, in order to collect the data and compare them with experimental results. The comparison was made with the NRMSE (Normalized Root Mean Square Error), in order to identify the computer with the highest prediction horizon. Tests performed in 4 different configurations showed the difficulties of simulation reproducibility in LtSpice. The methodology developed was efficient in identifying the computer with better performance, which allows applying it to other cases in the literature. Resumo: Um dos aspectos essenciais da ciênciaé a habilidade de que trabalhos científicos possam ser reproduzidos. Essa característica permite que pesquisadores possam compreender, aprimorar ou mesmo questionar trabalhos que foram desenvolvidos por outros cientistas. Na teoria de controleé amplamente reconhecido a importância da modelagem e simulação de sistemas. Apesar deste reconhecimento, percebe-se uma menor atenção nos efeitos da precisão finita dos computadores na reprodutibilidade de simulação de sistemas dinâmicos não-lineares. Neste trabalho, apresenta-se um estudo de caso da reprodutibilidade na simulação de um circuito caótico Jerk, utilizando o software LtSpice. Para isso foram realizadas simulações do circuito em uma mesma versão do software em diferentes computadores, a fim de coletar os dados e compará-los com resultados experimentais. A comparação foi feita com oíndice NRMSE (Normalized Root Mean Square Error ), com o objetivo de identificar o computador com o maior horizonte de predição. Testes realizados em 4 configurações distintas evidenciaram as dificuldades da reprodutibilidade de simulação no LtSpice. A metodologia desenvolvida foi eficiente em identificar o computador com melhor desempenho, o que permite aplicá-la para outros casos da literatura.
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