Duffing映射的全局动力学行为分析与研究

摘要

针对二维离散Duffing映射,分别以a和b为分岔参数,借助多重分岔图、吸引子共存分析和吸引域分析等手段,对该映射系统的全局动力学行为进行了深入研究.研究结果表明,离散Duffing系统仅在一定参数范围内收敛;且随着参数的变化,虽然系统收敛区域的范围和收敛域中的动力学行为各不相同,但其变化均具有一定的规律性.最后,借助吸引子、吸引域及边界的分析,明确了共存吸引子间的关系及其变化规律,进一步探讨了系统不同动力学行为间的转迁机制.%For the two-dimensional discrete Duffing map, the global dynamics is studied in depth by analyzing the multi-bifurcation diagrams, coexisting attractors, attraction basins, etc.The numerical results shows that Duffing map only converges in the certain regions of parameters, and the convergence regions are varying with the change of parameters.Although the dynamic behavior are complex, its evolution is of a certain regularity with the changing parameters.Finally, based on the analysis of attractors, attraction basins and basin boundaries, the relation and variation of coexisting attractors are explored, and the transformation mechanism between different dynamic behaviors in Duffing map is further investigated.