A Probabilistic Theory of Nonlinear Dynamical Systems Based on the Cell State Space Concept

[+] Author and Article Information
C. S. Hsu

Department of Mechanical Engineering, University of California, Berkeley, Calif. 94720

J. Appl. Mech 49(4), 895-902 (Dec 01, 1982) (8 pages) doi:10.1115/1.3162633 History: Received January 01, 1982; Online July 21, 2009


Developed in the paper is a probabilistic theory for nonlinear dynamical systems. The theory is based on discretizing the state space into a cell structure and using the cell probability functions to describe the state of a system. Although the dynamical system may be highly nonlinear the probabilistic formulation always leads to a set of linear ordinary differential equations. The evolution of the probability distribution among the cells can then be studied by applying the theory of Markov processes to this set of equations. It is believed that this development possibly offers a new approach to the global analysis of nonlinear systems.

Copyright © 1982 by ASME
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