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COBEM 2021
26th International Congress of Mechanical Engineering
A Julia code for computing basins of attraction of one-degree-of-freedom systems
Submission Author:
Guilherme Franzini , SP
Co-Authors:
Rodrigo Provasi, Vitor Schwenck Franco Maciel, Guilherme Franzini
Presenter: Vitor Schwenck Franco Maciel
doi://10.26678/ABCM.COBEM2021.COB2021-0454
Abstract
A plethora of phenomena on dynamics are governed by nonlinear equations. In some cases, the linearization of the mathematical model can lead to results without physical sense. In the last three decades, the sensitivity of the response of nonlinear equations with respect to changes in the initial conditions has received numerous research efforts. In this scenario, the definition of the basins of attraction is a key aspect that demands significant computational efforts. Although the use of high-level languages simplifies the implementation, it may not lead to acceptable performance, thus leaning development to lower-level languages. Recently, Julia language has been developed aiming to combine the benefits of high-level programming environments, especially ease of use, with the performance of lower-level languages. The present paper focuses on presenting a numerical code programmed in Julia for obtaining basins of attraction of a one degree-of-freedom oscillator. The performance of the code is compared with its C++ counterpart for classical Helmholtz-Duffing oscillator for different values of the forcing amplitude.
Keywords
basins of attraction, Julia language, nonlinear dynamics
