Title :
Bifurcations in nonlinear systems-computational issues
Author :
Alvarado, Fernando L.
Author_Institution :
Wisconsin Univ., Madison, WI, USA
Abstract :
An examination is made of computational issues associated with singular Jacobian and Hopf bifurcations in large nonlinear systems. Singular Jacobian bifurcations can be computed effectively using the point of collapse method. Hopf bifurcations can be computed using a Kronecker sum to reduce the problem to the computation of a singular Jacobian. However, this is shown to be computationally intensive. An alternative method for the computation of Hopf bifurcations based on the point of collapse method together with a complex expansion of the problem is presented
Keywords :
nonlinear network analysis; nonlinear systems; numerical methods; Hopf bifurcations; Jacobian bifurcations; Kronecker sum; complex expansion; computational issues; computationally intensive; nonlinear systems; point of collapse method; Bifurcation; Eigenvalues and eigenfunctions; Jacobian matrices; Nonlinear equations; Nonlinear systems; Topology;
Conference_Titel :
Circuits and Systems, 1990., IEEE International Symposium on
Conference_Location :
New Orleans, LA
DOI :
10.1109/ISCAS.1990.112246
