On the Stability of Equilibrium Paths Associated With Autonomous Systems

[+] Author and Article Information
K. Huseyin

Department of Systems Design, University of Waterloo, Waterloo, Ontario, N2L 3G1, Canada

J. Appl. Mech 48(1), 183-187 (Mar 01, 1981) (5 pages) doi:10.1115/1.3157564 History: Received March 01, 1980; Revised July 01, 1980; Online July 21, 2009


The postcritical behavior and stability distribution on the equilibrium paths emanating from a divergence point associated with an autonomous system are studied within a state-space formulation. The analysis concerning the stability of equilibrium paths is based on the eigenvalues of the Jacobian evaluated at arbitrary equilibrium points in the vicinity of a critical point. Explicit conditions of stability and instability concerning the initial and postcritical paths are obtained through a perturbation approach. It is shown that at an asymmetric point of bifurcation an exchange of stabilities between two paths occurs in complete analogy with conservative systems. Similarly, a symmetric point of bifurcation involves a postcritical path which is totally stable (unstable) if the initial path is unstable (stable).

Copyright © 1981 by ASME
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