S. A. M. Martins

B. C. Silva, F. L. Milani, E. G. Nepomuceno et al.

Computational techniques are extensively applied in nonlinear science. However, while the use of computers for research has been expressive, the evaluation of numerical results does not grow in the same pace. Hammel et al. (Journal of Complexity, 1987, 3(2), 136--145) were pioneers in the numerical reliability field and have proved a theorem that a pseudo-orbit of a logistic map is shadowed by a true orbit within a distance of $10^{-8}$ for $10^{7}$ iterates. But the simulation of the logistic map with less than 100 iterates presents an error greater than $10^{-8}$ in a modern computer, performing a test based on the concept of multiple pseudo-orbits and symbolic computing.

M. L. C. Peixoto, E. G. Nepomuceno, H. M. Rodrigues et al.

Differences between computer simulation of dynamical systems and laboratory experiments are common in teaching and research in engineering. Normally, numerical inaccuracy and the non-ideal behaviour of the devices involved in the experiment are the most common explanations. With the application of interval analysis, it is possible to incorporate the numerical and parametric uncertainties in the simulation, allowing a better understanding of the play between simulation and experiment. This article presents a case study in which an step input is applied to an RLC circuit. Using the toolbox Intlab for Matlab, it was possible to present a computer simulation with the range that encompasses the experimental results . Comparison of simulation with experimental data show the success of the technique and indicates a potential content to be delivered to undergraduate engineering courses.

W. R. Lacerda Junior, S. A. M. Martins, E. G. Nepomuceno

This work presents a new meta-heuristic approach to select the structure of polynomial NARX models for regression and classification problems. The method takes into account the complexity of the model and the contribution of each term to build parsimonious models by proposing a new cost function formulation. The robustness of the new algorithm is tested on several simulated and experimental system with different nonlinear characteristics. The obtained results show that the proposed algorithm is capable of identifying the correct model, for cases where the proper model structure is known, and determine parsimonious models for experimental data even for those systems for which traditional and contemporary methods habitually fails. The new algorithm is validated over classical methods such as the FROLS and recent randomized approaches.