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- Dynamics and stability results of fractional integro-differential equations with complex order

pp. 119–127 | DOI: 10.5890/DNC.2018.06.001

D. Vivek, K. Kanagarajan, S. Harikrishnan

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In this paper, we study the existence, uniqueness and Ulam stability of solutions of fractional integro-differential with complex order. Based on Krasnoselkii ﬁxed point theorem and Banach contraction principle, we obtain existence and Ulam stability results.

- Nonlinear Time Series Analysis of Complex Systems Using an e-Science Web Framework

pp. 129-141 | DOI: 10.5890/DNC.2018.06.002

Bruno B. F. Leonor, Walter A. dos Santos, Asiel Bomﬁn Jr., Reinaldo R. Rosa

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The analysis of time series in the era of Big Data has become a major challenge for computational framework research. Furthemore, in the areas of space science which deals with a large variety of data, the practical consistence between workload, workﬂow and cloud computing is crucial. Here, such consistence is provided by an innovativee-Science framework project named Sentinel which is based on a NoSQL data base (MongoDB) and a containerization platform (Docker). This web framework supports researchers for time series analysis in a cloud environment where they can easily access, parameterize, initialize and monitor their applications. As a case study in the Brazilian Space Weather Program, we consider the intensive analysis of time series from a complex information system for solar activity monitoring and forecasting. As a prototype for implementing the framework, the DFA (detrended ﬂuctuation analysis) techniquewas used as a nonlinear spectrum analyzer applied to the solar irradiance measurements from 1978 to 2012. Moreover, new applications can be added and managed by researchers on the portal easily to complement their data analysis purposes.

- Simulating the Interaction of a Comet With the Solar Wind Using a Magnetohydrodynamic Mode

pp. 143-149 | DOI: 10.5890/DNC.2018.06.003

Edgard de F. D. Evangelista†, Margarete O. Domingues, Odim Mendes, Oswaldo D. Miranda

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We present simulations of a comet interacting with the solar wind. Such simulations are treated in the framework of the ideal,2D magnetohydrodynamics (MHD), using the FLASH code in order to solve the equations of such a formalism. Besides, the cometis treated as a spherically symmetric source of ions in the equations of MHD. We generate results considering several scenarios, using different values for the physical parameters of the solar wind and of the cometin each case. Our aim is to study the inﬂuence of the solar wind on the characteristics of the comet and, given the nonlinear nature of the MHD, we search for the occurrence of phenomena which are typical of nonlinear systems such as instabilities and turbulence.

- Using RQA for evaluating heart rate patterns under controlled breathing

pp. 151-163 | DOI: 10.5890/DNC.2018.06.004

Guênia Ladeira, Luís Cláudio Oliveira-Lopes, Gabriela V. Lima

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In this work, the variation of time and amplitude of the electrical stimulation of the heart muscle is analyzed during respiratory control exercise, effect of the autonomic nervous system. The speciﬁcs are veriﬁed by recurrence plot, and recurrence quantiﬁcation analysis. The analysis revealed distinguished behavior of the electrical stimulation of the heart. And, the cross recurrence between the variations of amplitude and time demonstrated the equilibrium relationship in the cardiac cycles, which are accentuatedin the exerciseof concentration.

- Using Different Interval Extensions to Increase the Accuracy of the Exact Solution on Recursive Functions

pp. 165-172 | DOI: 10.5890/DNC.2018.06.005

H. M. Rodrigues Junior, M. L. C. Peixoto, M. E.G. Nepomuceno., S.A.M. Martins

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The results obtained by numerical computation are not always precise. It happens because a computer has storage limitations and its set of numbers is ﬁnite. In this work, the interval analysis is used to give bounds around exact solution of the logistic map function. The connection between computer and interval mathematics makes possible to solve problems that can not be solved efﬁciently using ﬂoating point arithmetic. We use the intersection of different pseudo-orbits obtained by interval extensions to reduce the bounds of the exact solution. The method is applied using the Intlab toolbox. Without any substantial computational effort, we show a reduction of up to 26% in the width of interval by applying the method proposed in this paper.

- Semantic networks of keywords from Brazilian dissertations on physics teaching

pp. 173-183 | DOI: 10.5890/DNC.2018.06.006

J. O. do Nascimento, R. L. S. Monteiro, D. M. Moreira, M. A. M. Simões Gonçalves, H. B. de Barros Pereira

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Metrics of social and complex networks can be used in the study of emergent patterns in semantic networks. The goal of this article is to analyze the semantic network formed by the keywords of theses and dissertations on physics teaching that were defended in Brazil between the years 1996 and 2006. We describe the method used for constructing the network, including the keywords. We analyze the network’s properties in local and global contexts. We study which keywords are presented as cut points, since their removal from the network result in a number of components greater than one. Our results suggest that the networkis small–world and scale–free. In addition, using the proposed method, we veriﬁed that most of the topics emphasized in the network are related to the education of physics instructors andnotto methods of teaching physics at different levels.

- Exploiting the rounding mode of ﬂoating-point in the simulation of Chua’s circuit

pp. 185-193 | DOI: 10.5890/DNC.2018.06.007

M. R. Silva, E. G. Nepomuceno, G. F. V. Amaral, S. A. M. Martins, L. G. Nardo

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The Chua’s circuit has been considered as one of the most important paradigms for nonlinear science studies. Its simulations is usually undertaken by means of numerical methods under the rules of IEEE 754-2008 ﬂoating-point arithmetic standard. Although, it is well known the propagation error issue, less attention has been given to its consequences on the simulation of Chua’s circuit. In this paper we presented a simulation technique for the Chua’s circuit, it exhibits qualitative differences in traditional approaches such as RK3, RK4 and RK5. By means of the positive largest Lyapunov exponent we show that for the same initial condition and same set of parameters, we produce a periodical and a chaotic solution.

- Nonlinear integral inequalities with parameter and bounded solutions of dynamical systems

pp. 195-207 | DOI: 10.5890/DNC.2018.06.008

Taouﬁk Ghrissi, M. A. Hammami

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We present in this paper some new nonlinear integral inequalities with parameter and we will use them to show the boundedness of solutions of perturbed nonlinear time-varying differential equations. Furthermore, some examples are given to illustrate the applicability of the obtained results.

- Polar Ampliﬁcation Projected by Energy Balance Model with Nonlinear Parametrization of Outgoing Longwave Radiation

pp. 209-223 | DOI: 10.5890/DNC.2018.06.009

Dmitry V. Kovalevsky, Genrikh V. Alekseev

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A linear energy balance model (EBM) of polar ampliﬁcation (PA) developed by Langen and Alexeev (2007) is modiﬁed by replacing the conventional linear parametrization of outgoing longwave radiation (OLR) with a more accurate nonlinear (quadratic) approximation for OLR.The nonlinear version of the model is studied analytically and numerically. The numerical results presented in the paper convincingly demonstrate the importance of adopting the nonlinear approximation for parametrizing the OLR in EBMs. The simulation results yielded by the nonlinear version of the model are visibly different from those provided by the linear model, especially for simulations of climate change in high latitudes and for quantiﬁcation of PA with dedicated indices.