Nonlinear Dynamics

, Volume 77, Issue 3, pp 467–479 | Cite as

A parallelized multi-degrees-of-freedom cell mapping method

  • R. P. Eason
  • A. J. Dick
Original Paper


Cell mapping methods, in general, provide a computationally efficient way to analyze the long-term global dynamics of lower-dimensional systems. The multi-degrees-of-freedom cell mapping (MDCM) method, in particular, overcomes the scaling limitations of other cell mapping methods, allowing efficiency benefits to be realized for higher-dimensional systems. Unfortunately, the sequential structure of the MDCM algorithm limits the ability to utilize the parallel processing capabilities of modern computers. In this paper, the parallelized multi-degrees-of-freedom cell mapping (PMDCM) method is introduced. The PMDCM method features a restructured algorithm that employs parallel computation to streamline one of the most time-consuming elements: numerical integration. The PMDCM algorithm is described in detail and is demonstrated by comparing results produced by the PMDCM method to those produced by MDCM and the grid-of-starts. By using the PMDCM method on a quad-core processor with 100 simultaneous integrations per mapping step, the total computation time is reduced by 93 %, as compared with the MDCM method. With PMDCM, the global integrity measure also agrees more closely with the computationally intensive grid-of-starts method when compared with the MDCM method.


Multi-DOF cell mapping (MDCM) Global dynamic analysis  Basin of attraction Bi-stability 


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Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringRice UniversityHoustonUSA

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