Automatic Selection Of Poincaré Cross-section Research And Observation System Design

The Poincare section method,as an important method for observing nonlinear systems,can significantly reduce the difficulty of studying nonlinear systems.Choosing a suitable plane as the Poincare section is the key to applying the Poincare section method,and also the difficulty in using the Poincare section method.To solve this problem,this paper proposes a method for automatically selecting a suitable plane as a Poincare section.In this method,any plane in the phase space is represented by a specific time-domain signal through projection,and the three outputs of the nonlinear system are analyzed in the time domain,so that the Poincare section can be directly selected in the time domain.In addition,this paper summarizes the selection conditions of the plane signal through theoretical analysis,and quickly calculates the appropriate plane parameters according to the selection conditions of the plane signal,thereby realizing the function of automatically selecting the Poincare section in real time.In this paper,the projection time domain method is proposed firstly,which transforms the process of selecting the Poincare section into the time domain.Through theoretical analysis,the conditions for judging whether the selected plane is a suitable Poincare section in the time domain are summarized.We have also carried out simulation experiments to prove the feasibility and effectiveness of selecting Poincare cross section in the time domain.After that,we used the selection conditions of plane signals in the time domain to construct an equation system,and obtained the appropriate plane parameters by solving the equation system.Finally,FPGA is used to build a hardware system that automatically selects Poincare sections,and simulation experiments are conducted to verify that the functions of each module can be implemented correctly.