Routh-Hurwitz criterion in the examination of eigenvalues of a system of nonlinear ordinary differential equations
Year: 1987
Type: article
Abstract: In stability analysis of nonlinear systems, the character of the eigenvalues of the Jacobian matrix (i.e., whether the real part is positive, negative, or zero) is needed, while the actual value of the eigenvalue is not required. We present a simple algebraic procedure, based on the Routh-Hurwitz criterion, for determining the character of the eigenvalues without the need for evaluating the eigenvalues explicitly. This procedure is illustrated for a system of nonlinear ordinary differential equations we have studied previously. This procedure is simple enough to be used in computer code, and, more importantly, makes the analysis possible even for those cases where the secular equation cannot be solved.
Source: Physical Review A
Authors: Edmund X. DeJesus, Charles Kaufman
Institutions: Boston University, University of Rhode Island
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2109677272