This paper introduces the development of several cell mapping methods closely associated with nonlinear stochastic dynamical systems, including generalized cell mapping method with digraph, cell mapping method based on shorttime Gaussian approximation, parallel cell mapping method etc. The applications of cell mapping method in stochastic dynamical systems are also shown, focusing on stochastic response、bifurcation、exit and vibroimpact system. Finally, some challenges and possible future researches about cell mapping method are presented.
徐伟,岳晓乐,韩群.胞映射方法及其在非线性随机动力学中的应用[J].动力学与控制学报,2017,15(3):200~208; Xu Wei, Yue Xiaole, Han Qun. Cell mapping method and its applications in nonlinear stochastic dynamical systems[J]. Journal of Dynamics and Control,2017,15(3):200-208.