Interpolated Cell Mapping of Dynamical Systems

[+] Author and Article Information
B. H. Tongue

Department of Mechanical Engineering, University of California, Berkeley, CA 94720

K. Gu

School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332

J. Appl. Mech 55(2), 461-466 (Jun 01, 1988) (6 pages) doi:10.1115/1.3173700 History: Received November 26, 1986; Revised October 16, 1987; Online July 21, 2009


A method is proposed to efficiently determine the basins of attraction of a nonlinear system’s different steady-state solutions. The phase space of the dynamical system is spacially discretized and the continuous problem in time is converted to an iterative mapping. By means of interpolation procedures, an improvement in the system accuracy over the Simple Cell Mapping technique is achieved. Both basins of attraction for a representative nonlinear system and characteristic system trajectories are generated and compared to exact solutions.

Copyright © 1988 by ASME
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