| 摘 要： | In this paper,the general characteristics and the topological consideration of theglobal behaviors of higher order nonlinear dynamical systems and the characteristics of theapplication of cell-to-cell mapping method in this analysis are expounded.Specifically,theglobal analysis of a system of two weakly coupled van der Poloscillators using cell-to-cellmapping method is presented.The analysis shows that for this system,there exist two stable limit cycles is 4-dimensional state space,and the whole 4-dimensional state space is divided into two almostequal parts which are,respectively,the two asymptotically stable domains of attraction ofthe two periodic motions of the two stable limit cycles.The validities of these conclusiosabout the global behaviors are also verified by direct lng term numerical integration.Thus.it can be seen that the cell-to-cell mapping method for global analysis of fourth ordernonlinear dynamical systems is quite effective.
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