Poincare Linear Interpolated Cell Mapping: Method for Global Analysis of Oscillating Systems

[+] Author and Article Information
J. Levitas, T. Weller

Faculty of Aerospace Engineering, Technion—Israel Institute of Technology, 32000 Haifa, Israel

J. Appl. Mech 62(2), 489-495 (Jun 01, 1995) (7 pages) doi:10.1115/1.2895956 History: Received February 19, 1993; Revised August 31, 1993; Online October 30, 2007


A method for global analysis of nonlinear dynamical oscillating systems was developed. The method is based on the idea of introducing a Poincare section into a multidimensional state space of the dynamical system and combine it with an interpolation procedure within the cells which constitute the discretized problem domain of interest. The proposed method was applied to study the global behavior of two nonlinear coupled van der Pol oscillators. Significant saving in calculation time, in comparison with both direct numerical integration and Poincare-like simple cell mapping, is demonstrated.

Copyright © 1995 by The American Society of Mechanical Engineers
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