FPGA-based Arbitrary Angle Poincaré Cross-section Circuit Design

In recent years, nonlinear dynamics are considered as a hotspot in nonlinear discipline. From the theoretical analysis to application development, scientists gradually grasp the characteristics of nonlinear dynamical systems and analytical method, depth study of nonlinear dynamics of motion characteristics and exploited. The Poincare section method as one of the important methods of nonlinear dynamics research is used to analysis and judgment the complexity of on all kinds of nonlinear dynamics state. This design is mainly based on FPGA control point of view of Poincare section, the analysis of motion characteristics of the system under test through the intercept point oscilloscope display, which can obverse the cutoff point on the Poincare section in under test system.Firstly, a systematic analysis is applied in the nonlinear dynamics theory and the Poincare section method, and a realizing method of this design is proposed in this paper. Secondly, the built of Chua test system, the design of Poincare section hardware circuitry, the design of the FPGA control circuit, the design sampling keeping circuit and other parts are made a detailed analysis, simulation and test, which ensure correctly and feasibly for each part of the design. The correctness of the design is verified by using MATLAB simulation software. Finally, the whole circuit is tested and successfully analyzed the display results of the motion of the system under test on the oscilloscope.