Analysis for the reconstruction of attractors by reconstruction of phase spaces using delay times

Abstract Being able to estimate the behavior of a system from observable data is one of the great difficulties that any system presents. This problem presents a challenge for researchers who perform scenario estimation and forecasting. In most problems it is proposed to perform data analysis, but in this article, we propose to perform synthesis in such a way that a dipheomorphic attractor is constructed. that models the system. In the treatment of the analysis, we start from the inputs and assume some equations that describe the system, in the case of synthesis the most important thing is the data produced by the system, since these are real with some associated noise, so from those data and using Takens’ theorem, we can build an attractor that models the system we model in a more real way.