Deflation techniques for the determination of periodic solutions of a certain period |
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| Authors: | VS Kalantonis EA Perdios AE Perdiou O Ragos MN Vrahatis |
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| Institution: | 1. Department of Engineering Sciences, University of Patras, GR-25000, Patras, Greece
2. Department of Mathematics, University of Patras, GR-25000, Patras, Greece
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| Abstract: | The computation of periodic orbits of nonlinear mappings or dynamical systems can be achieved by applying a root-finding method. To determine a periodic solution, an initial guess should be located within a proper area of the mapping or a surface of section of the phase space of the dynamical system. In the case of Newton or Newton-like methods these areas are the basins of convergence corresponding to the considered solution. When several solutions of the same period exist in a particular region, then the deflation technique is suitable for the calculation of all these solutions. This technique is applied here to the Hénon's mapping and the driven conservative Duffing's oscillator. |
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