中文摘要：

通过改变耦合函数将模态分解法进行了推广，应用于非恒同耦合系统同步的研究．详细研究了周期吸引子、概周期吸引子等非恒同耦合系统的同步，得到了同步的局部渐近稳定性条件．并进行了数值模拟，发现同步时动力学现象丰富．概周期吸引子耦合系统会出现稳定的周期、概周期同步解，由于耦合周期吸引子耦合系统会出现多个稳定的周期同步解，且其吸引域差别较大，均出现了同步的多值性．同时也验证了该方法的正确性．

英文摘要：

In this paper the mode decomposition approach in the studies of the synchronization of the coupled dynamical systems is generalized to the case of the coupled non-identical dynamical systems by changing the coupling function. The synchronization of the non-identical periodic and quasi-periodic attractor systems is considered detailedly and the conditions for their local synchronization stability are obtained in this paper. The numerical simulation is performed and it was found that the dynamical behaviors of the synchronization are rich. The behaviors include stable synchronized periodic and quasi-periodic solutions in the coupled non-identical quasi-periodic attractor systems, and several stable synchronized periodic solutions in the coupled non- identical periodic attractors, where the new stable synchronized periodic solutions are born due to the coupling, and their attraction basins differe greatly, i. e., in both of them the multiplicity of the synchronization appears. At the same time the validity of the mode decomposition is also verified.