Analysis and Research on the Global Dynamical Behavior of Duffing Map

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.